The addition principle of equality states that if a = b, then a + c = b + c.

When you solve equations using this addition principle of equality, you need to use the additive inverse property. In other words, you must add the same number to both sides of an equation.

**Example #1:**

x - 5 = 10

x - 5 + 5 = 10 + 5 We add the opposite of (-5) to both sides of the equation.

x + 0 = 15 We simplify -5 + 5 = 0.

x = 15 The solution is x = 15

To check the answer, simply substitute 15 in for x, in the original equation and solve.

15 - 5 = 10

10 = 10

Example #2:

x + 12 = -5

x + 12 + (- 12) = -5 + (- 12) We add the opposite of (+12) to both sides of the equation.

x + 0 = -17 We simplify +12 - 12 = 0.

x = -17 The solution is x = -17

Check our answer.

(-17) + 12 = -5

-5 = -5