# Multi–Step Equations

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

## 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.

### 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: $$→x=14$$

### 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 $$3: 3x=10→3 x \ ÷ \ 3=\frac{10}{3}→x=\frac{10}{3}$$

### 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: $$-2+x+2=5+2 →x=7$$

### 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

### 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. $$\color{blue}{3x – 18 = 22 + x – 3 + x}$$

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