### Multi-Step Equations with Like Terms

When we look at a linear equation we see two kinds of terms: those that contain the unknown variable, and those that don’t. When we look at an equation that has an **combining like terms**. The terms with an **like terms** because they contain the same variable (or, as you will see in later chapters, the same combination of variables).

Like Terms |
Unlike Terms |
---|---|

#### Using the Distributive Property of Multiplication

To add or subtract like terms, we can use the Distributive Property of Multiplication.

To solve an equation with two or more like terms, we need to combine the terms first.

#### Solving for Unknown Values

1. Solve

There are two like terms: the

Subtracting 8 from both sides gives us

And finally, multiplying both sides by -1 gives us

2. Solve

This problem requires us to deal with fractions. We need to write all the terms on the left over a common denominator of six.

Then we subtract the fractions to get

Finally we multiply both sides by 6 to get

### Example

#### Example 1

Solve

This problem requires us to deal with fractions. We need to write all the terms on the left over a common denominator of ten.

Then we subtract the fractions to get

Finally we multiply both sides by

to get

### Review

Solve the following equations for the unknown variable.

1.3x−0.7x=12 −10a−2(a+5)=14 5(2y−3y)=−20 23x−15x=1415 5x−(3x+2)=1 s−3s8=56 10(y+5y)=10 2.3x+2(0.75x−3.5)=7.5 3(x+2)+5(2−x)=−32 6x+2(5x−2)=12

### Review (Answers)

To view the Review answers, open this PDF file and look for section 3.5.