### Solving Equations Using Addition and Subtraction

When we work with an algebraic equation, it’s important to remember that the two sides have to stay equal for the equation to stay true. We can change the equation around however we want, but whatever we do to one side of the equation, we have to do to the other side. In the introduction above, for example, we could get from the first equation to the second equation by subtracting 22 from both sides:Similarly, we can add numbers to each side of an equation to help solve for our unknown.

**Example 1**

*Solve*.

**Solution**

To solve an equation for , we need to

**isolate**that is, we need to get it by itself on one side of the equals sign. Right now our has a 3 subtracted from it. To reverse this, we’ll add 3—but we must add 3 to

**both sides.**

**Example 2**

*Solve*

**Solution**

It doesn’t matter what the variable is—the solving process is the same.

Make sure you understand the addition of decimals in this example!

**Example 3**

*Solve*.

**Solution**

To isolate , we need to subtract from both sides.

Now we have to subtract fractions, which means we need to find the LCD. Since 5 and 7 are both prime, their lowest common multiple is just their product, 35.

Make sure you’re comfortable with decimals and fractions! To master algebra, you’ll need to work with them frequently.

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