Expressions & Equations
GradesGrade 7Expressions & EquationsSolving Multi-Step Equations & Inequalities

Solving Multi-Step Equations & Inequalities

✏️ Expressions & Equations
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Solving Multi-Step Equations & Inequalities

Balance both sides of an equation — and flip the inequality when multiplying or dividing by a negative.

Solving a multi-step equation means using inverse operations to isolate the variable. Solving an inequality follows the same steps, with one critical rule: if you multiply or divide both sides by a negative number, the inequality sign reverses.

2x+5=112x=16x=82x + 5 = -11 \Rightarrow 2x = -16 \Rightarrow x = -8
🔑Multi-step equation with fractions
Solve: (3/4)x − 2 = 7

Add 2 to both sides: (3/4)x = 9
Multiply both sides by 4/3: x = 9 × (4/3) = 12
34x2=734x=9x=943=12\frac{3}{4}x - 2 = 7 \Rightarrow \frac{3}{4}x = 9 \Rightarrow x = 9 \cdot \frac{4}{3} = 12
Inequality with sign flip
Solve: −3x + 1 > 10

−3x > 9
Divide by −3 and FLIP the sign: x < −3
3x+1>103x>9x<3-3x + 1 > 10 \Rightarrow -3x > 9 \Rightarrow x < -3
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Remember This!

Always flip the inequality sign when you multiply or divide both sides by a negative number. Forgetting this is the most common inequality mistake!

✏️ Try It!

Solve: −2(x + 3) = 14. What is x?

Take Quiz 📝 — 25 Questions