One Step Inequalities Worksheets with Answer Key - Free Printable

Let’s solve each inequality one by one. We’ll isolate the variable (like k, y, n, etc.) on one side of the inequality sign. Then we’ll write the solution and describe how to graph it.

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Problem ①: k - 5 ≥ -14

Add 5 to both sides:
k - 5 + 5 ≥ -14 + 5
→ k ≥ -9

Graph: On a number line, put a closed circle at -9 (because ≥ includes -9), and shade everything to the right.

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Problem ②: 6 + y ≥ -3

Subtract 6 from both sides:
6 + y - 6 ≥ -3 - 6
→ y ≥ -9

Graph: Closed circle at -9, shade right.

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Problem ③: n + 5 > -3

Subtract 5 from both sides:
n + 5 - 5 > -3 - 5
→ n > -8

Graph: Open circle at -8 (because > does NOT include -8), shade right.

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Problem ④: v - 6 ≤ -14

Add 6 to both sides:
v - 6 + 6 ≤ -14 + 6
→ v ≤ -8

Graph: Closed circle at -8, shade left.

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Problem ⑤: b/6 ≤ -4

Multiply both sides by 6:
(b/6) × 6 ≤ -4 × 6
→ b ≤ -24

Graph: Closed circle at -24, shade left.

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Problem ⑥: -7n > 0

Divide both sides by -7 → BUT remember: when you divide or multiply by a negative number, flip the inequality sign!

-7n / (-7) < 0 / (-7)
→ n < 0

Graph: Open circle at 0, shade left.

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Problem ⑦: -12 > l - 7

This is the same as: l - 7 < -12 (just flipped for easier solving)

Add 7 to both sides:
l - 7 + 7 < -12 + 7
→ l < -5

Graph: Open circle at -5, shade left.

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Problem ⑧: -13x < -156

Divide both sides by -13 → FLIP the inequality sign!

(-13x)/(-13) > (-156)/(-13)
→ x > 12

Check: -156 ÷ -13 = 12? Yes, because 13×12=156, and negative ÷ negative = positive.

Graph: Open circle at 12, shade right.

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Final Answer:

① k ≥ -9
② y ≥ -9
③ n > -8
④ v ≤ -8
⑤ b ≤ -24
⑥ n < 0
⑦ l < -5
⑧ x > 12