Two-Step Inequalities Worksheets with Answer Key - Free Printable

Since both ExplainAnswer and TeachTopic are false, we will only provide the Final Answer after solving all 8 inequalities step by step.

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We’ll solve each inequality one at a time, then describe how to graph the solution (even though we can’t draw here, we’ll note key points like open/closed circle and direction).

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Problem 1: -a - 2 > 8

Step 1: Add 2 to both sides
→ -a > 10

Step 2: Multiply both sides by -1 → remember to flip the inequality sign!
→ a < -10

Graph: Open circle at -10, arrow pointing left.

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Problem 2: -11p - 4 > -15

Step 1: Add 4 to both sides
→ -11p > -11

Step 2: Divide by -11 → flip the inequality
→ p < 1

Graph: Open circle at 1, arrow pointing left.

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Problem 3: 27 ≤ 7x + 6

Step 1: Subtract 6 from both sides
→ 21 ≤ 7x

Step 2: Divide by 7
→ 3 ≤ x or x ≥ 3

Graph: Closed circle at 3, arrow pointing right.

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Problem 4: 8k + 6 ≤ 94

Step 1: Subtract 6
→ 8k ≤ 88

Step 2: Divide by 8
→ k ≤ 11

Graph: Closed circle at 11, arrow pointing left.

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Problem 5: 1 + 4x ≤ 31

Step 1: Subtract 1
→ 4x ≤ 30

Step 2: Divide by 4
→ x ≤ 7.5

Graph: Closed circle at 7.5, arrow pointing left.

*(Note: On number line, 7.5 is halfway between 7 and 8)*

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Problem 6: 3r + 3 ≥ -12

Step 1: Subtract 3
→ 3r ≥ -15

Step 2: Divide by 3
→ r ≥ -5

Graph: Closed circle at -5, arrow pointing right.

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Problem 7: -4 < (x - 2)/2

Step 1: Multiply both sides by 2
→ -8 < x - 2

Step 2: Add 2 to both sides
→ -6 < x or x > -6

Graph: Open circle at -6, arrow pointing right.

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Problem 8: (-9 + a)/15 > 1

Step 1: Multiply both sides by 15
→ -9 + a > 15

Step 2: Add 9 to both sides
→ a > 24

Graph: Open circle at 24, arrow pointing right.

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Final Answer:

① a < -10
② p < 1
③ x ≥ 3
④ k ≤ 11
⑤ x ≤ 7.5
⑥ r ≥ -5
⑦ x > -6
⑧ a > 24