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Back to Use variables to represent quantities and construct equations and inequalities to solve problems

Solving Equations and Inequalities

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Grade 7·~35 min·Common Core Math - Grade 7·standard·7-ee-b-4
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Solve 8x=568x = 56. What is the value of xx?

2.

Evaluate −3.5×(−4)-3.5 \times (-4).

3.

Which expression is equivalent to 5(x+4)5(x + 4)?

B

Fluency Practice

1.

Solve 4x+7=314x + 7 = 31. Enter the value of xx.

2.

Solve 34x−2=7\dfrac{3}{4}x - 2 = 7. Enter the value of xx.

3.

Solve 3(x+5)=243(x + 5) = 24. Enter the value of xx.

Two number lines comparing open circle (endpoint not included, for strict inequalities) vs. closed circle (endpoint included, for non-strict inequalities), both using a generic reference point with leftward arrows.
4.

Solve 2x+1<72x + 1 < 7. How should the solution be shown on a number line?

5.

Solve −2x+3≥9-2x + 3 \geq 9. Which inequality represents the solution?

C

Varied Practice

1.

Which equation is equivalent to 4(x+3)=284(x + 3) = 28?

2.

Solve 12x−5=3\dfrac{1}{2}x - 5 = 3 step by step.
After adding 5 to both sides: 12x=\dfrac{1}{2}x =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
After multiplying both sides by 2: x=x =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

value of (1/2)x:
value of x:
Number line from -8 to 1 with a solid (closed) circle at -4 and a bold arrow pointing left, indicating the solution region x ≤ -4.
3.

A number line shows a closed circle at −4-4 with shading extending to the left. Which inequality does this graph represent?

4.

A parking lot can hold at most 60 cars. Let cc = the current number of cars in the lot. Which inequality represents this situation?

5.

Solving an inequality gives the solution n≥5n \geq 5. Which statement correctly describes all solutions?

D

Word Problems

1.

Priya rents a bicycle for $2.50 per hour plus a one-time helmet fee of $5. She paid $17.50 in total. Let xx = the number of hours she rented the bicycle.

1.

Which equation represents this situation?

2.

Solve 2.50x+5=17.502.50x + 5 = 17.50. How many hours did Priya rent the bicycle?

2.

Five friends split the cost of a shared meal equally. Each friend also paid $1.50 for their own drink. Each person paid $8.50 in total. Let xx = the cost per person for the shared meal (not including drinks).

Use the equation 5(x+1.50)=5×8.505(x + 1.50) = 5 \times 8.50 to find the cost per person for the shared meal.

Number line from 0 to 8 with a closed circle at 6 and a leftward arrow, representing the solution to Kenji's spending constraint.
3.

Kenji has $30 to spend at a craft fair. Admission costs $6, and each item he buys costs $4. Let nn = the number of items Kenji can buy.

1.

Which inequality represents the total amount Kenji can spend?

2.

Solve the inequality 4n+6≤304n + 6 \leq 30. What is the maximum number of items Kenji can buy?

3.

What does the solution n≤6n \leq 6 mean in this situation?

4.

The temperature outside is 8°F and dropping at 3 degrees per hour. A water pipe will freeze when the temperature reaches −4°F or lower. Let hh = the number of hours from now.

Write and solve an inequality to find when the pipe may freeze. State the minimum whole-number value of hh, and identify whether you needed to flip the inequality symbol and why.

E

Error Analysis

Error contrast card: Jaylen wrote x > -2 (incorrect, red X) vs. correct answer x < -2 with flip noted (checkmark). Bottom banner: 'Divide by negative → flip the symbol'.
1.

Jaylen solved the inequality −3x+5>11-3x + 5 > 11:

−3x+5>11-3x + 5 > 11
−3x>6-3x > 6
x>−2x > -2

Jaylen's answer: x>−2x > -2

What error did Jaylen make?

Error contrast card: Maya subtracted 3 first (wrong, giving x = 3.4) vs. two correct methods — divide by 5 first (x = 1) or distribute first (x = 1).
2.

Maya solved 5(x+3)=205(x + 3) = 20:

5(x+3)−3=20−35(x + 3) - 3 = 20 - 3
5x=175x = 17
x=3.4x = 3.4

Maya's answer: x=3.4x = 3.4

What was Maya's first error?

F

Challenge / Extension

1.

Solve 23(x−6)=−4\dfrac{2}{3}(x - 6) = -4. Enter the exact value of xx.

2.

Marcus works as a part-time delivery driver. He earns $12.50 per hour and receives a fixed fuel reimbursement of $6 per shift. Marcus wants to earn more than $75 on his next shift. Let hh = the number of hours he works.

1.

Which inequality represents the condition Marcus must meet?

2.

Solve 12.50h+6>7512.50h + 6 > 75. What is the minimum whole number of hours Marcus must work?

0 of 25 answered