Solving Equations

Using Addition and Subtraction

After studying this lesson, you will be able to:

• Solve equations using addition and subtraction.

A mathematical statement that contains an equal sign is called an equation .

Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

2. Collect like terms on each side of the equal sign

3. Isolate the variable by undoing the operation

4. Check by substituting the solution into the original equation

The equal sign divides equations into 2 parts or 2 sides. Equations are like balance scales. Whatever is done to one side, must be done to the other side in order to maintain equality or balance.

Example 1

Check:

substitute -15 for z in the original equation

(-15) + 6 = -9

-9 = -9

Example 2

Check:

substitute 6 for x in the original equation

6 - (-4) = 10 (remember to "add the opposite")

10 = 10

Example 3

Check:

substitute -4 for p in the original equation

(-4) - (-2) = -2 (remember to add the opposite)

-4 + 2 = -2

-2 = -2

Example 4

Check:

substitute 7.4 for x in the original equation (7.4) + (-2.1) = 5.3

5.3 = 5.3