How to Solve Multi-Step Equations? (+FREE Worksheet!)
Solving multi-step equations require two or more mathematics operations. Learn how to solve multi-step equations in a few simple steps.
Related Topics
- How to Solve One-Step Equations
- How to Solve One-Step Inequalities
- How to Solve Multi-Step Inequalities
- How to Solve Systems of Equations
- How to Graph Single–Variable Inequalities
Step by step guide to solve multi-step equations
- Combine “like” terms on one side.
- Bring variables to one side by adding or subtracting.
- Simplify using the inverse of addition or subtraction.
- Simplify further by using the inverse of multiplication or division.
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Multi–Step Equations – Example 1:
Solve this equation. \(-(8 \ – \ x)=6\)
Solution:
First use Distributive Property: \(−(8 \ − \ x)= − 8 \ + \ x\)
Now solve by adding \(8\) to both sides of the equation. \(−8 \ + \ x=6 →−8 \ + \ x \ +8=6 +\ 8 \)
Now simplify: \(→x=14\)
Multi–Step Equations – Example 2:
Solve this equation. \(2x \ + \ 5=15 \ – \ x\)
Solution:
First, bring variables to one side by adding \(x\) to both sides.
\(2x \ + \ 5=15 \ − \ x→ 2x \ + \ 5 +x=15 \ – \ x +x → 3x \ + \ 5=15\). Now, subtract \(5\) from both sides:
\(3x+5=15 → 3x \ + \ 5 \ − \ 5=15 \ − \ 5→3x=10\)
Now, divide both sides by \(3: 3x=10→3 x \ ÷ \ 3=\frac{10}{3}→x=\frac{10}{3}\)
Multi–Step Equations – Example 3:
Solve this equation. \( -(2-x)=5\)
Solution:
First use Distributive Property: \( -(2-x)=-2+x\)
Now solve by adding \(2\) to both sides of the equation. \(-2+x=5 →-2+x+2=5+2 \)
Now simplify: \(-2+x+2=5+2 →x=7\)
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Multi–Step Equations – Example 4:
Solve this equation. \(4x+10=25-x\)
Solution:
First, bring variables to one side by adding \(x\) to both sides.
\(4x+10=25-x → \) \( 4x+10+x=25-x+x→5x+10=25\) . Now, subtract \(10\) from both sides:
\(5x+10=25 → 5x+10-10=25-10→5x=15 \)
Now, divide both sides by \(5: 5x=15 →5x÷5=\frac{15}{5}→x=3\)
Exercises for Solving Multi–Step Equations
Solve each equation.
- \(\color{blue}{– (2 – 2x) = 10}\)
- \(\color{blue}{– 12 = – (2x + 8)}\)
- \(\color{blue}{3x + 15 = (– 2x) + 5}\)
- \(\color{blue}{– 28 = (– 2x) – 12x}\)
- \(\color{blue}{2 (1 + 2x) + 2x = – 118}\)
- \(\color{blue}{3x – 18 = 22 + x – 3 + x}\)
Download Multi-Step Equations Worksheet
Answers
- \(\color{blue}{6}\)
- \(\color{blue}{2}\)
- \(\color{blue}{-2}\)
- \(\color{blue}{2}\)
- \(\color{blue}{-20}\)
- \(\color{blue}{37}\)
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