Inequalities Worksheets - Free Printable

Let’s solve each inequality step by step.

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1a. Solve: -10 ≥ -8w - 12

Step 1: Add 12 to both sides to isolate the term with w.
-10 + 12 ≥ -8w - 12 + 12
→ 2 ≥ -8w

Step 2: Divide both sides by -8.
⚠️ Remember: When you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign!

2 ÷ (-8) ≤ w
→ -¼ ≤ w
or written as: w ≥ -¼

✔ Final answer for 1a: w ≥ -0.25

Plot on number line: Closed circle at -0.25, shade to the right.

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1b. Solve: r/1 ≤ -9 · (-1)

Step 1: Simplify the right side.
-9 × (-1) = 9
So: r ≤ 9

✔ Final answer for 1b: r ≤ 9

Plot on number line: Closed circle at 9, shade to the left.

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2a. Solve: -5 ≥ 6n - 7

Step 1: Add 7 to both sides.
-5 + 7 ≥ 6n - 7 + 7
→ 2 ≥ 6n

Step 2: Divide both sides by 6 (positive, so no flipping).
2 ÷ 6 ≥ n
→ ⅓ ≥ n
or: n ≤ ⅓

✔ Final answer for 2a: n ≤ 0.333...

Plot on number line: Closed circle at 1/3, shade to the left.

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2b. Solve: -2(u - 3) ≥ 10

Step 1: Distribute the -2.
-2·u + (-2)·(-3) ≥ 10
→ -2u + 6 ≥ 10

Step 2: Subtract 6 from both sides.
-2u + 6 - 6 ≥ 10 - 6
→ -2u ≥ 4

Step 3: Divide both sides by -2 → ⚠️ Flip the inequality sign!
u ≤ 4 ÷ (-2)
→ u ≤ -2

✔ Final answer for 2b: u ≤ -2

Plot on number line: Closed circle at -2, shade to the left.

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Final Answer:
1a. w ≥ -0.25
1b. r ≤ 9
2a. n ≤ 1/3
2b. u ≤ -2