Inequalities & Graphing
Multi-Step Inequalities
Solve multi-step inequalities like equations — but remember: when you multiply or divide both sides by a negative number, FLIP the inequality sign!
Watch & Learn
Watch a clear, friendly video explanation of Multi-Step Inequalities:
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Solve: 3x + 4 > 13
Step-by-Step Solution
Subtract 4 from both sides: 3x > 9
Divide both sides by 3 (positive, no flip): x > 3
Answer
x > 3
Problem
Solve: −2x + 6 ≤ 12
Step-by-Step Solution
Subtract 6 from both sides: −2x ≤ 6
Divide by −2 — FLIP the sign! x ≥ −3
Answer
x ≥ −3
Problem
Solve: 5x − 3 < 2x + 9
Step-by-Step Solution
Subtract 2x: 3x − 3 < 9
Add 3: 3x < 12
Divide by 3: x < 4
Answer
x < 4
Problem
Solve: −5x + 10 ≥ 25
Step-by-Step Solution
Subtract 10 from both sides: −5x ≥ 15
Divide by −5 — FLIP the sign! x ≤ −3
Answer
x ≤ −3
Problem
Solve: 3(x + 2) > 18
Step-by-Step Solution
Distribute: 3x + 6 > 18
Subtract 6: 3x > 12
Divide by 3 (positive, no flip): x > 4
Answer
x > 4
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Solve: 4x − 5 > 11
Solve: −3x ≤ 15
Solve: 2x + 7 ≥ 3x − 1
Solve: 6x + 2 < 20
Solve: −4x + 8 > 0
Solve: 5x − 10 ≥ 0
Solve: −2x + 4 < 10
Solve: 3x + 6 ≤ 0
Solve: 7 − x > 3
Solve: 2(x + 3) ≤ 14
Solve: −x + 5 ≥ 9
Solve: 4x − 1 < 3x + 5
Finished all 12? Give yourself a pat on the back — then check your work!
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