Matching worksheet for solving inequalities from word problems.

Let’s solve each problem step by step and match it to the correct answer.

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Problem 1: Solve 3.5x + 10 < -30

Subtract 10 from both sides:
→ 3.5x < -40

Divide both sides by 3.5:
→ x < -40 / 3.5
→ x < -11.428... → approximately x < -11.43

That matches option d.

✔ Problem 1 → d

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Problem 2: Michelle has $100. She wants to buy paper pins ($20), file covers ($20), and paper weights ($10 each). How many paper weights can she purchase?

She spends $20 + $20 = $40 on pins and covers.

Leftover money: $100 - $40 = $60

Each paper weight is $10 → 60 ÷ 10 = 6

✔ Problem 2 → a

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Problem 3: Richard buys tooth cleaning kit ($25) and toothbrush ($15). He has $80 total. Spends rest on body soap at $5 each. How many soaps?

Spent on kit and brush: $25 + $15 = $40

Leftover: $80 - $40 = $40

Each soap is $5 → 40 ÷ 5 = 8

✔ Problem 3 → e

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Problem 4: Solve -0.8x - 6 < -10

Add 6 to both sides:
→ -0.8x < -4

Divide both sides by -0.8 → remember to flip inequality when dividing by negative!

→ x > (-4)/(-0.8)
→ x > 5

✔ Problem 4 → b

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Problem 5: Solve 1.6 + 4x > 14

Subtract 1.6 from both sides:
→ 4x > 12.4

Divide by 4:
→ x > 3.1

✔ Problem 5 → f

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Problem 6: Jennifer has $60. Buys rice ($14) and cold drinks ($10). Rest on pizza at $4 each. How many pizzas?

Spent on rice and drinks: $14 + $10 = $24

Leftover: $60 - $24 = $36

Each pizza is $4 → 36 ÷ 4 = 9

✔ Problem 6 → c

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Problem 7: Angela has $75. Buys doorbell ($15). Rest on hockey sticks at $5 each. How many sticks?

Leftover after doorbell: $75 - $15 = $60

Each stick is $5 → 60 ÷ 5 = 12

✔ Problem 7 → g

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Final Answer:
1-d, 2-a, 3-e, 4-b, 5-f, 6-c, 7-g