How to Solve Multi-Step Equations

How to Solve Multi-Step Equations

Solving multi-step equations require two or more mathematics operations. Learn how to solve multi-step equations in few simple steps.

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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.

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.
\(2x \ + \ 5=15 \ − \ x→3x \ + \ 5=15\). Now, subtract \(5\) from both sides:
\(3x \ + \ 5 \ − \ 5=15 \ − \ 5→3x=10\)
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: \(-2+x+2=5+2 →x=7\)

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.
\( 4x+10+x=25-x+x→5x+10=25\) . Now, subtract \(10\) from both sides:
\(5x+10-10=25-10→5x=15 \)
Now, divide both sides by \(5: 5x=15 →5x÷5=\frac{15}{5}→x=3\)

Exercises for Solving Multi–Step Equations

Solve each equation.

  1. \(\color{blue}{– (2 – 2x) = 10}\)
  2. \(\color{blue}{– 12 = – (2x + 8)}\)
  3. \(\color{blue}{3x + 15 = (– 2x) + 5}\)
  4. \(\color{blue}{– 28 = (– 2x) – 12x}\)
  5. \(\color{blue}{2 (1 + 2x) + 2x = – 118}\)
  6. \(\color{blue}{3x – 18 = 22 + x – 3 + x}\)

Download Multi-Step Equations Worksheet

This image has an empty alt attribute; its file name is answer-3.png

Answers

  1. \(\color{blue}{6}\)
  2. \(\color{blue}{2}\)
  3. \(\color{blue}{-2}\)
  4. \(\color{blue}{2}\)
  5. \(\color{blue}{-20}\)
  6. \(\color{blue}{37}\)

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