Two-step Inequalities Worksheet Answer Key – Grade 7

Problem 1 Add, Then Divide

Subtract 4: 3x > 15. Divide by 3: x > 5. Test 6: 3(6) + 4 = 22, and 22 > 19.

x > 5

Problem 2 Subtract, Then Divide

Add 7: 2x < 16. Divide by 2: x < 8. Test 7: 2(7) − 7 = 7, and 7 < 9.

x < 8

Problem 3 Graph a Simple Inequality

Place an open circle at 3 and shade to the left, toward the numbers less than 3.

Open circle at 3, ray to the left

Problem 4 A Quotient Inequality

Subtract 2: x5 > 4. Multiply by 5: x > 20.

x > 20

Problem 5 First Negative Coefficient

Subtract 3: −2x > 8. Divide by −2 and reverse the sign: x < −4. Test −5: −2(−5) + 3 = 13, and 13 > 11.

x < −4

Problem 6 Negative Coefficient with Subtraction

Add 10: −5x < 30. Divide by −5 and reverse the sign: x > −6. Test 0: −10 < 20 is true.

x > −6

Problem 7 Decimal Coefficient

Add 2.5: 0.5x < 5.5. Divide by 0.5: x < 11.

x < 11

Problem 8 Decimals on Both Sides of the Sign

Subtract 3.6: 1.2x > 6. Divide by 1.2: x > 5. Test 6: 1.2(6) + 3.6 = 10.8, and 10.8 > 9.6.

x > 5

Problem 9 Fraction Coefficient

Subtract 3: 56x > 10. Multiply by 65, a positive number, so the sign stays: x > 12. Test 18: 56(18) + 3 = 18, and 18 > 13.

x > 12

Problem 10 Negative Quotient

Subtract 1: −x4 > 2. Multiply by −4 and reverse the sign: x < −8.

x < −8

Problem 11 Parentheses and a Positive Factor

Divide by 3: x − 2 > 4. Add 2: x > 6. Test 7: 3(5) = 15 > 12.

x > 6

Problem 12 From Graph to Inequality

The circle is open at −1 and the ray goes left: x < −1.

For 2x + 5 < 3, subtract 5 to get 2x < −2, then divide by 2 to get x < −1, which matches the graph.

x < −1

Problem 13 Negative Factor Outside

Divide by −2 and reverse the sign: x + 3 > −5. Subtract 3: x > −8. Test 0: −2(3) = −6 < 10.

x > −8

Problem 14 Variable on the Right Side

Subtract 7: 11 > −2.5x. Divide by −2.5 and reverse the sign: −4.4 < x, which is x > −4.4. Test 0: 18 > 7 is true.

x > −4.4

Problem 15 Club Fundraiser Goal

8n + 60 > 240. Subtract 60: 8n > 180. Divide by 8: n > 22.5.

Shirts are whole numbers, and 22 shirts give only $236, so the least is 23 (8 × 23 + 60 = 244).

23 shirts

Problem 16 Texting Plan Budget

20 + 0.05t < 35. Subtract 20: 0.05t < 15. Divide by 0.05: t < 300.

Fewer than 300 texts

Problem 17 Diver Ascent

−12 + 4m > −2. Add 12: 4m > 10. Divide by 4: m > 2.5.

More than 2.5 minutes

Problem 18 Bus Rental Budget

2.25m + 150 < 375. Subtract 150: 2.25m < 225. Divide by 2.25: m < 100.

Test 99: 2.25(99) + 150 = 372.75, which is under 375.

Fewer than 100 miles

Problem 19 Draining the Pool

600 − 15t < 270. Subtract 600: −15t < −330. Divide by −15 and reverse the sign: t > 22.

Test 23: 600 − 345 = 255, which is under 270.

More than 22 minutes

Problem 20 Markers with Tax

4(m + 1.25) < 30. Divide by 4: m + 1.25 < 7.5. Subtract 1.25: m < 6.25.

Test 6: 4(7.25) = 29, under 30.

Each pack must cost less than $6.25