7.EE.B.4Common CoreMathExpressions and EquationsGrade 7
7.EE.B.4: Solving Word Problems with Equations and Inequalities
In plain English: 7.EE.B.4 is the Common Core grade 7 math standard that asks students to use a variable for an unknown amount in a word problem, then write and solve a simple equation or inequality about it. Equations have the form px + q = r or p(x + q) = r, and inequalities compare px + q with r using greater than or less than, with rational numbers. Students graph inequality solutions on a number line and explain what they mean.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
a.Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
b.Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Common Core State Standards for Mathematics · Domain: Expressions and Equations (EE) · Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Also written as 7.EE.4 · Official standard
Students turn word problems into two-step equations and inequalities and solve them. A variable is a letter, such as x, that stands for an unknown number. An equation says two amounts are equal, and an inequality says one amount is greater than or less than another. Grade 7 uses equations of the form px + q = r and p(x + q) = r, and inequalities of the form px + q > r or px + q < r. The letters p, q and r stand for rational numbers: whole numbers, fractions, decimals and their negatives.
For equations, students solve each problem two ways: with arithmetic (working backward from the answer, with no variable) and with algebra (doing the same thing to both sides of the equation). Then they compare the order of the operations in each method. For inequalities, students graph the solution set on a number line and decide which numbers make sense in the story, for example only whole numbers of sales. The variable appears on one side only. Equations with the variable on both sides come in grade 8 (8.EE.C.7).
Learning Objectives
By the end of this lesson, students will be able to:
Choose a variable for an unknown quantity in a word problem and say what it stands for, with units
Write and solve equations of the form px + q = r and p(x + q) = r with whole numbers, fractions, decimals and negative numbers
Solve the same problem with arithmetic and with algebra, and name the order of the operations in each
Write and solve inequalities of the form px + q > r or px + q < r, including a negative p, which reverses the inequality sign
Graph an inequality's solution set on a number line and explain which solutions make sense in the problem
Prior Knowledge Required
Students should already be comfortable with:
Solving one-step equations of the form x + p = q and px = q 6.EE.B.7
Writing inequalities such as x > c and showing them on a number line 6.EE.B.8
Adding, subtracting, multiplying and dividing positive and negative rational numbers 7.NS.A.3
The distributive property, for example 3(x + 2) = 3x + 6 6.EE.A.3
Write this number puzzle on the board and ask students to find the number in their heads or on scrap paper:
Warm-Up Prompt
"I think of a number. I multiply it by 4, then add 7. The result is 43. What is my number? Explain how you found it."
Many students work backward: 43 - 7 = 36, then 36 ÷ 4 = 9. Write their steps on the board as the arithmetic solution. Then ask: "How could we write the puzzle as a math sentence?" Let n be the number. The puzzle says 4n + 7 = 43. Point out that working backward undid the operations in reverse order: the puzzle added 7 last, so students subtracted 7 first. Check: 4(9) + 7 = 43.
Direct Instruction20 minutes
Part 1: Equations (standard a). Show the four steps students use on every word problem:
Name the unknown: write "Let m = the number of months" with units. This is the variable.
Write the equation or inequality: find the amount that changes (the coefficient p, the number multiplied by the variable) and the fixed amount (the constant q).
Solve: undo the operations in reverse order, doing the same thing to both sides.
Check and answer: substitute the value back into the story, and answer the question in a sentence with units.
Work through the examples below. For the first two, solve with arithmetic first, then with algebra, and write both next to each other so students can compare the operations.
px + q = r, compared with arithmetic
A gym charges a $25 sign-up fee plus $15 per month. Maya paid $115 in all. How many months did she pay for? Let m = the number of months.
Equation: 15m + 25 = 115. Arithmetic: 115 - 25 = 90, then 90 ÷ 15 = 6. Algebra: subtract 25 from both sides (15m = 90), then divide both sides by 15 (m = 6). Same operations, same order: 6 months.
p(x + q) = r, the official example
The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Let w = the width in cm.
Equation: 2(w + 6) = 54. Arithmetic: 54 ÷ 2 = 27, then 27 - 6 = 21. Algebra: divide both sides by 2 (w + 6 = 27), then subtract 6 (w = 21). The width is 21 cm.
px + q = r with a negative rate
At midnight the temperature was 6°F. It dropped 1.5°F every hour. After how many hours was it -3°F? Let h = the number of hours.
Equation: -1.5h + 6 = -3. Subtract 6: -1.5h = -9. Divide by -1.5: h = 6. It was -3°F after 6 hours, at 6 a.m.
Inequality, the official example
A salesperson is paid $50 per week plus $3 per sale. This week they want their pay to be at least $100. Let s = the number of sales.
Equation: 50 + 3s ≥ 100, so 3s ≥ 50 and s ≥ 16⅔. Sales are whole numbers, so they need 17 or more sales.
px + q < r
A class trip must cost less than $200. The bus costs $80, and each student ticket costs $7.50. How many students can go? Let x = the number of students.
Equation: 7.50x + 80 < 200, so 7.50x < 120 and x < 16. At most 15 students can go.
For the rectangle, show a second algebra route: distribute first to get 2w + 12 = 54, subtract 12 (2w = 42) and divide by 2 (w = 21). This route subtracts before it divides, so its order is different from the arithmetic solution, but the answer is the same. Diagram 1 shows the arithmetic route as a tape diagram, a drawing that shows amounts as bars split into parts.
Part 2: Inequalities (standard b). A solution set is the set of all numbers that make an inequality true. Solve an inequality the same way as an equation, with one new rule: when you multiply or divide both sides by a negative number, reverse the inequality sign. Test it with numbers: 2 < 5 is true, but after multiplying both sides by -1, -2 < -5 is false, and -2 > -5 is true.
To graph, use an open circle when the boundary number (the number where the solutions start) is not a solution (< or >) and a closed circle when it is (≤ or ≥, as in "at least"). Then shade the side that holds the solutions. Diagram 2 graphs the salesperson example. Ask: "Is 16⅔ sales possible? Which numbers on the graph make sense?" Only the whole numbers 17, 18, 19 and so on. The official example says "at least," which uses ≥. The solving steps are the same as for >, and only the circle changes.
Guided Practice15 minutes
Pairs solve four problems. Partner A solves with algebra and Partner B with arithmetic (for the equations), then they compare their steps. Circulate and ask each pair to say the order of their operations out loud.
Guided practice problems with answers
Problem
Answer
3(x - 4) = 27
x = 13 (27 ÷ 3 = 9, then 9 + 4 = 13)
(1/2)x + 5 = 12
x = 14 (12 - 5 = 7, then 7 ÷ (1/2) = 14)
-2(x + 3) = 10
x = -8 (10 ÷ (-2) = -5, then -5 - 3 = -8)
A phone battery is at 90% and loses 6% per hour of video. For how many hours h does it stay above 30%?
90 - 6h > 30, so -6h > -60 and h < 10: fewer than 10 hours
Listen for these errors: dividing only one term by p in p(x + q) = r, forgetting to reverse the sign when dividing by -6, and writing the constant q where the rate p belongs. For the battery problem, ask: "Can h be 4.5? Can it be negative?" (Yes, time can be any number from 0 up to 10, but not negative.)
Independent Practice15 minutes
Students solve six problems on their own to build fluency. For each equation, they check by substitution. For each inequality, they graph the solution set on a number line and test one number from the shaded part.
Independent practice problems with answers
Problem
Answer
5x - 8 = 47
x = 11
4(y + 2.5) = 30
y = 5
-3x + 7 = 19
x = -4
(2/3)(k - 6) = 8
k = 18
12 + 4n > 40
n > 7 (open circle at 7, shade right)
20 - 2.5t < 5
t > 6 (open circle at 6, shade right; the sign reverses)
Closure5 minutes
Exit ticket: (1) Solve 8(x - 1.5) = 20 two ways, and write the order of the operations for each. (Answer: x = 4. Arithmetic: divide by 8, then add 1.5. Distributing: 8x - 12 = 20, add 12, then divide by 8.) (2) Solve and graph (1/4)x + 3 < 5. (Answer: x < 8, open circle at 8, shaded left.) (3) In one sentence: when do you reverse the inequality sign?
Differentiation Strategies
For Struggling Students
Draw a tape diagram, like Diagram 1, before writing any equation, so students see the equal parts and the fixed part
Start with whole numbers, then change one number to a decimal or a fraction once the steps feel easy
Give a "last in, first out" card: the operation done last to x is the first one to undo
For Advanced Students
Ask students to write a word problem whose equation has a negative p and a fractional answer, and to explain what the answer means
Give an inequality problem with two limits, for example a gift card that must keep more than $5 and a plan that must last at least 3 weeks, and ask which limit matters
Ask when the arithmetic route and the distribute-first route use the same order of operations, and when they do not
Assessment Guidance
What to Look For
Check that students write what the variable stands for, with units, before they write the equation. In the arithmetic-versus-algebra comparison, students should name each operation in order (for example "subtract 25, then divide by 15") and say whether the two lists match. For inequalities, look for the reversed sign after dividing by a negative number, the right circle (open for < and >, closed for ≤ and ≥), and a final sentence that answers the question with numbers that make sense, such as whole tickets.
02
Classroom Activities
3 Activities
1
Two Ways Card Sort
15 minPairs
Pairs match each story card with its equation card and its arithmetic card, then solve with algebra and compare the order of the operations. There are 12 cards: 4 story cards, 4 equation cards and 4 arithmetic cards.
Story Cards
S1: Ava buys 3 notebooks that cost the same and one $4 pen. She spends $13. What does one notebook cost?
S2: Five friends order pizza. Each friend pays an equal share of the food plus $2 toward the tip, and together they pay $45. What is one share of the food?
S3: A diver is 30 m below the surface (-30 m) and rises 4.5 m each minute. After how many minutes is she at -3 m?
S4: A baker makes 2 batches of a mix. Each batch uses some flour plus 0.5 cup of sugar. The two batches use 7 cups in all. How much flour is in one batch?
In S1 and S3, the arithmetic subtracts first and then divides. Does the algebra solution use the same order?
In S2 and S4, the arithmetic divides first. What happens to the order if you distribute first instead?
What does your variable stand for in each card? Say it with units.
Modification for Distance Learning
Put the 12 cards on a shared slide. Pairs drag each equation and arithmetic card next to its story, then type the algebra steps in a text box.
2
Floor Number Line
20 minGroups of 3-4
Tape a number line from 0 to 30 on the floor. Each group gets two of the six inequality cards, writes and solves the inequality, and then shows the solution set on the floor line with a sticky-note circle and a strip of tape.
Inequality Cards
C1: A streaming plan costs a $15 fee plus $9 per month. The total must stay under $96. (9m + 15 < 96, so m < 9: up to 8 whole months)
C2: On a winter morning the air is at -8°C and warms 2°C per hour. When is it above 4°C? (2h - 8 > 4, so h > 6: after 6 hours)
C3: A hiker has 18 km left and walks 4 km per hour. When is the distance left less than 6 km? (18 - 4h < 6, so h > 3; the sign reverses)
C4: Leo has $30 and saves $12 each week. When does he have more than $150? (12w + 30 > 150, so w > 10: 11 weeks or more)
C5: A freight elevator holds less than 1,000 kg. The operator weighs 90 kg and each box weighs 35 kg. (35b + 90 < 1,000, so b < 26: at most 25 boxes)
C6: A phone bill is $10 plus $0.25 per text. When is the bill more than $16? (0.25t + 10 > 16, so t > 24: 25 texts or more)
Procedure
Groups write "Let ___ = ___" for each card before writing the inequality
A group member stands on the boundary number, and the group decides: open circle or closed circle?
The group lays tape in the direction of the solutions, or places dots only on whole numbers when only whole numbers make sense
Another group tests one number from the shaded part in the original story
Discussion Questions
Four cards (C1, C4, C5, C6) count whole things. Why do their graphs use dots instead of a shaded line?
C2 and C3 measure time. Is 6.5 hours a solution to C2? Is 3.25 hours a solution to C3?
Which card needed the sign to be reversed, and why?
Challenge Variation
Groups rewrite one card so that the answer changes from "at most" to "at least", then trade with another group and solve the new card.
3
Story Builder
15 minPairs
Pairs work in reverse: they get an equation or inequality and write a real-world story that fits it. This builds the first part of the standard, using variables to represent quantities.
Procedure
Each pair gets three cards: 6x + 10 = 70, 3(x + 4) = 36 and 25 - 2x > 9
For each card, write a story from everyday life (money, sports, recipes, school events) and a sentence "Let x = ..."
Solve each card (x = 10, x = 8, x < 8) and write the answer as a sentence about the story
Trade stories with another pair; they write their own equation from your story and check that it matches the card
Discussion Questions
In your story for 3(x + 4) = 36, what does the 4 stand for, and why is it inside the parentheses?
For 25 - 2x > 9, does your story allow x = 7.5? Why or why not?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Tape Diagram for the Rectangle Problem
The perimeter of 54 cm splits into two equal parts, each one length plus one width. Taking the 6 cm length away from each part of 27 cm leaves the width, 21 cm. The bars are drawn to scale, 10 pixels per centimeter, and show the arithmetic route: divide by 2, then subtract 6.
Diagram 2: Graphing the Salesperson Inequality
The top line graphs the solution set of 50 + 3s ≥ 100. The closed circle at 16⅔ shows that the boundary is included, and the shading shows every larger number. The bottom line keeps only the answers that make sense: whole numbers of sales from 17 up. Drawn to scale.
04
Homework Assignment
~30 min
7.EE.B.4 Homework: Equations and Inequalities from Word Problems
Directions: Show all work. For each word problem, write "Let ___ = ___" before you write the equation or inequality. Check every equation by substitution. Graph every inequality on a number line and answer the question in a full sentence.
A coach orders 6 team jerseys. Each jersey costs the same, plus $3 per jersey to print a name. The total bill is $132. Write an equation of the form p(x + q) = r and find the price of one jersey without a name. Solve it once with arithmetic and once with algebra, then list the operations each method used, in order.
Part 2: Word Problems with Equations (Problems 3-4)
A bike rental costs $8.50 plus $4.25 per hour. Jordan paid $25.50. Define a variable, write an equation, and find how many hours Jordan rented the bike.
An isosceles triangle has two sides of equal length and a base of 10 cm. Its perimeter is 38 cm. Write and solve an equation to find the length of each equal side.
Part 3: Inequalities (Problems 5-6)
Maria has $75 on her lunch card and spends $4.50 each school day. She wants to keep more than $12 on the card. Write and solve an inequality for the number of days d. Graph the solution set, then say how many full school days she can buy lunch.
A moving van rents for $40 plus $0.80 per mile. Your family's budget is less than $100. Write and solve an inequality for the miles m, graph it, and explain which values of m make sense.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Variables and Setup
Variable defined with units; equation or inequality matches the story
Correct setup but variable not defined
Setup missing or does not match
Solving
All steps shown and correct, sign reversed when needed
One arithmetic or sign error
Most answers incorrect
Arithmetic vs. Algebra
Both methods shown with operations listed in order
Both methods shown, order not described
Only one method
Graph and Meaning
Correct circle and shading; answer makes sense in the story
Graph correct but no sentence, or sentence ignores whole numbers
Graph missing or incorrect
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Fair tickets cost $12 each, and parking costs $10. Kim spent $70 in all. Which equation can you use to find t, the number of tickets she bought?
Answer: A
Each ticket adds $12, so the tickets cost 12t, and parking adds $10 once: 12t + 10 = 70 (t = 5). Choice B switches the rate and the fixed cost. Choice C charges the $10 parking on every ticket. Choice D adds the parking to the total instead of taking it away.
Question 2 of 20 · Multiple Choice
Solve 9x - 14 = 49.
Answer: C
Add 14 to both sides: 9x = 63. Divide by 9: x = 7. Check: 9(7) - 14 = 49. Choice A subtracts 14 instead of adding it (49 - 14 = 35) and then divides by 9. Choice B adds 14 correctly but forgets to divide by 9. Choice D subtracts 14 and does not divide.
Question 3 of 20 · Multiple Choice
Solve 5(x + 3) = 65.
Answer: B
Divide both sides by 5: x + 3 = 13. Subtract 3: x = 10. Check: 5(13) = 65. Choice A subtracts 3 from 65 before dividing, which ignores the parentheses: (65 - 3) ÷ 5 = 12.4. Choice C adds 3 instead of subtracting. Choice D stops after dividing by 5.
Question 4 of 20 · Multiple Choice
Ben solves 4(x - 2.5) = 18 with arithmetic: 18 ÷ 4 = 4.5, then 4.5 + 2.5 = 7. Which algebra steps use the same operations in the same order?
Answer: D
Ben divided by 4 first and added 2.5 second. In algebra, divide both sides by 4 (x - 2.5 = 4.5), then add 2.5 (x = 7). Choice A uses the same operations in the opposite order, which does not work here, because the 4 multiplies the whole x - 2.5. Choice B subtracts where Ben added. Choice C multiplies where Ben divided.
Question 5 of 20 · Multiple Choice
Solve -(2/3)x + 5 = -7.
Answer: A
Subtract 5: -(2/3)x = -12. Divide by -2/3, which is the same as multiplying by -3/2: x = 18. Check: -(2/3)(18) + 5 = -12 + 5 = -7. Choice B drops the negative sign of the coefficient and divides -12 by 2/3. Choice C multiplies -12 by -2/3 instead of dividing. Choice D adds 5 to -7 instead of subtracting it, then divides -2 by -2/3.
Question 6 of 20 · Multiple Choice
Solve 14 - 3x > 2.
Answer: B
Subtract 14: -3x > -12. Divide by -3 and reverse the sign: x < 4. Test x = 0: 14 > 2 is true. Choice A forgets to reverse the sign. Choice C reverses the sign but gets -12 ÷ (-3) wrong: it is 4, not -4. Choice D adds 14 to 2 instead of subtracting it (-3x > 16), then divides.
Question 7 of 20 · Multiple Choice
The solution of 2x + 9 > 5 is x > -2. Which number line graph shows this solution set?
Answer: C
The boundary -2 is not a solution (2(-2) + 9 = 5, and 5 > 5 is false), so the circle is open. Numbers greater than -2 lie to the right. Choice A uses a closed circle, which would mean x ≥ -2. Choice B shades the numbers less than -2. Choice D puts the circle at 2 instead of -2.
Question 8 of 20 · Multiple Choice
Kai earns $8 per hour babysitting and has already saved $35. He wants to have more than $100 in all, and he is paid only for full hours. Solving 8h + 35 > 100 gives h > 8.125. What does the solution mean?
Answer: B
He needs more than 8.125 hours, and only full hours count, so the smallest answer is 9 hours: 8(9) + 35 = $107. Choice A rounds down: 8 hours gives 8(8) + 35 = $99, which is not more than $100. Choice C reverses the inequality. Choice D treats the inequality as an equation and ignores the full-hour rule.
Question 9 of 20 · Multiple Choice
A taxi charges $3.50 plus $2.25 per mile. Lena wants the fare to be less than $30. Which inequality describes the number of miles m she can ride?
Answer: D
The fare grows by $2.25 for each mile and starts at $3.50: 2.25m + 3.50 < 30, so m is less than about 11.8 miles. Choice A switches the rate and the starting fee. Choice B uses >, which means the fare is more than $30. Choice C adds the $3.50 to every mile.
Question 10 of 20 · Multiple Choice
Solve 0.4x + 1.6 < 5.2.
Answer: A
Subtract 1.6: 0.4x < 3.6. Divide by 0.4: x < 9. Choice B adds 1.6 instead of subtracting (0.4x < 6.8). Choice C reverses the sign, but 0.4 is positive, so the sign stays. Choice D multiplies 3.6 by 0.4 instead of dividing.
Question 11 of 20 · Multiple Choice
Solve -4(x - 1.5) = 26.
Answer: C
Divide both sides by -4: x - 1.5 = -6.5. Add 1.5: x = -5. Check: -4(-5 - 1.5) = -4(-6.5) = 26. Choice A subtracts 1.5 instead of adding it. Choice B divides by 4 instead of -4. Choice D multiplies only the x by -4 and leaves 1.5 alone: -4x + 1.5 = 26.
Question 12 of 20 · Multiple Choice
Four friends each buy a movie ticket and a $3.25 popcorn. They spend $59 in all. What does one ticket cost?
Answer: B
Let t = the ticket price: 4(t + 3.25) = 59. Divide by 4: t + 3.25 = 14.75. Subtract 3.25: t = 11.50. Choice A stops after dividing, which is the cost of a ticket and a popcorn together. Choice C subtracts only one popcorn from $59 before dividing by 4. Choice D subtracts one popcorn and forgets to divide.
Question 13 of 20 · Multiple Choice
A diver is at -40 m and rises 2.5 m per minute. After how many minutes t is she above -15 m? Solve -40 + 2.5t > -15.
Answer: A
Add 40 to both sides: 2.5t > 25. Divide by 2.5: t > 10, so after 10 minutes she is above -15 m. Choice B reverses the sign, but 2.5 is positive. Choice C subtracts 40 instead of adding it: 2.5t > -55. Choice D forgets to divide by 2.5.
Question 14 of 20 · Multiple Choice
A bowling alley charges $5 per game plus $4 for shoes. Noor spent $24 and writes 5g + 4 = 24. What does g stand for?
Answer: D
The 5 is the price of each game, so 5g is the cost of g games: g counts games (here g = 4). Choice A is the total, $24. Choice B is the rate, $5, the number multiplied by g. Choice C is the fixed amount, $4.
Solve 3(x + 1.5) = 21 in two ways: with arithmetic, and by distributing first. List the operations in order for each.
Arithmetic: 21 ÷ 3 = 7, then 7 - 1.5 = 5.5 (divide, then subtract). Distributing: 3x + 4.5 = 21, then 3x = 16.5, then x = 5.5 (subtract, then divide). Both give x = 5.5, but the order of the operations is different.
Question 17 of 20 · Short Answer
Cupcakes cost $2.50 each, and a gift box costs $3. Jada wants to spend less than $23 on one box and some cupcakes. Write and solve an inequality, graph it, and say how many cupcakes she can buy.
Let c = the number of cupcakes: 2.50c + 3 < 23, so 2.50c < 20 and c < 8. Graph: open circle at 8, shaded left, or dots at the whole numbers 0 to 7. She can buy at most 7 cupcakes: 7 cupcakes and the box cost $20.50, while 8 would cost exactly $23, which is not less than $23.
Question 18 of 20 · Short Answer
Solve (1/3)x - 3 > 2 and describe its graph.
Add 3: (1/3)x > 5. Multiply by 3: x > 15. Graph: an open circle at 15, shaded to the right. Test x = 18: 6 - 3 = 3, and 3 > 2 is true.
Question 19 of 20 · Short Answer
At 6 a.m. the temperature was -9°F. It rose by the same amount each hour and reached 15°F at noon, 6 hours later. Write and solve an equation to find how many degrees it rose each hour.
Let r = the rise per hour, in °F: 6r - 9 = 15. Add 9: 6r = 24. Divide by 6: r = 4. The temperature rose 4°F per hour. Check: -9 + 6(4) = 15.
Question 20 of 20 · Short Answer
A school needs seats for at least 150 people on a field trip. Two vans carry 12 people in all, and each bus holds 44 people. Write and solve an inequality for the number of buses b, and say how many buses to order.
Let b = the number of buses: 44b + 12 ≥ 150, so 44b ≥ 138 and b ≥ 3.14 (about). Buses come in whole numbers, so order 4 buses: 3 buses give only 3(44) + 12 = 144 seats, and 4 buses give 188 seats.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 7.EE.B.4 mean?
7.EE.B.4 means students can turn a word problem into a simple equation or inequality and solve it. The variable stands for the unknown amount, such as a number of months or a width in centimeters. Part a covers equations like 15m + 25 = 115 and 2(w + 6) = 54. Part b covers inequalities like 7.50x + 80 < 200, graphed on a number line and explained in the story.
What grade is 7.EE.B.4, and what comes after it?
It is a grade 7 standard in the Expressions and Equations domain. In grade 8, students solve equations with the variable on both sides and with like terms to collect (8.EE.C.7). In Algebra I, students solve any linear equation or inequality in one variable, including ones with letters as coefficients (HSA.REI.B.3).
What is the difference between an arithmetic solution and an algebraic solution?
An arithmetic solution works backward with numbers only, and an algebraic solution writes an equation and does the same thing to both sides. For the gym problem, arithmetic is 115 - 25 = 90, then 90 ÷ 15 = 6. Algebra is 15m + 25 = 115, then 15m = 90, then m = 6. The standard asks students to compare the two and name the order of the operations in each.
Why does the inequality sign flip when you divide by a negative number?
Multiplying or dividing by a negative number reverses the order of numbers on the number line. For example, 3 < 7, but -3 > -7. So in -5x < 20, dividing by -5 gives x > -4. Test x = 0: -5(0) = 0, and 0 < 20 is true, so 0 must be a solution, and it is greater than -4.
Should students distribute or divide first in p(x + q) = r?
Either way is correct, and the standard only asks students to solve these equations fluently. Dividing first often keeps the numbers smaller, as in 2(w + 6) = 54, where 54 ÷ 2 = 27. Distributing first is easier when p is a fraction whose product with q is a whole number. Comparing the two routes is a good way to see that the order of the operations can change while the answer stays the same.
Why is the answer to the inequality not always the answer to the problem?
The solution set of an inequality includes every number that works, but the story may allow only some of them. In the salesperson example, s ≥ 16⅔, but sales come in whole numbers, so the answer is 17 or more sales. Time, distance and money can take in-between values, while people, tickets and boxes cannot. Negative values often make no sense either.
Does 7.EE.B.4 include equations with variables on both sides?
No. In 7.EE.B.4 the variable appears once, in the form px + q = r or p(x + q) = r. Equations such as 3x + 5 = x + 11 belong to grade 8 (8.EE.C.7). Keep grade 7 practice to one variable term so students focus on setting up the equation from the story.
What are rational numbers, and why does the standard mention them?
A rational number is any number that can be written as a fraction of two integers, such as 3, -1.5, 0.25 or 2/3. The standard says p, q and r are rational numbers, so students solve equations with decimals, fractions and negative numbers, not only whole numbers. This builds on grade 7 work with operations on rational numbers (7.NS.A.3).
How can parents help with 7.EE.B.4 at home?
Parents can turn everyday costs into short puzzles. For example: "A ride costs $2 to start plus $1.50 per mile, and the trip cost $14. How many miles was it?" (8 miles.) Ask your child to say what the letter stands for, to solve it, and to check the answer by putting it back into the story.
What mistakes should teachers watch for?
A common mistake with p(x + q) = r is multiplying p by x only, for example rewriting 3(x + 5) = 24 as 3x + 5 = 24. Other frequent errors are forgetting to reverse the sign after dividing by a negative, using a closed circle for < or >, and giving an answer such as 16⅔ tickets that does not fit the story.
07
Related Standards
6 standards
These standards connect to 7.EE.B.4: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.EE.B.7Prerequisite
Solve real-world problems with equations x + p = q and px = q for nonnegative rationals
