Mrs.D Math · 7th Grade

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Model & Solve Two-Step Inequalities
Step 1: Undo + or −
→
Step 2: Undo × or ÷
+ Positive Coeff.
− Negative Coeff. (Flip!)
÷ Fraction Form
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📚 Two-Step Inequalities

The Two-Step Method

Solve just like a two-step equation — undo addition or subtraction first, then undo multiplication or division. The only difference: watch for the flip rule!

1
Add or subtract on both sides to isolate the variable term.
3x + 4 > 13 → subtract 4 → 3x > 9
2
Divide or multiply both sides to solve for x. Check the sign of the coefficient!
3x > 9 → divide by 3 → x > 3

⚠ The Flip Rule

In Step 2, if you divide or multiply both sides by a negative number, you must flip the inequality sign.

⚠ Example with negative coefficient
−2x + 6 ≤ 12
→ −6
−2x ≤ 6
→ ÷(−2) FLIP!
x ≥ −3

x/a + b form

1
Subtract b from both sides to isolate x/a.
x/3 + 5 < 11 → subtract 5 → x/3 < 6
2
Multiply both sides by a. Dividing by a positive — sign stays the same.
x/3 < 6 → multiply by 3 → x < 18
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TWO-STEP
⚠ Dividing by a negative — FLIP the sign!
Step 1
→
Step 2
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Two-step inequalities solved!

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