3.1 The Addition Property of Equality

To Solve an Equation means... To isolate the variable having a coefficient of 1 on one side of the equation. Ex: x = 5 is solved for x. y = 2x - 1 is solved for y.

Property of Equality You can add or subtract any number to BOTH sides of an equation and the equation will still hold true.

There are 3 key ideas to solving equations. An equation is a comparison of 2 equal quantities. Our goal is to solve for x. The Property of Equality – do the same thing to both sides of =.

An easy example: (don’t copy) Would you ever leave the house with only one shoe on? Would you ever put blush on just one cheek? Would you ever shave just one side of your face? We all know that 7 = 7. Does 7 + 4 = 7? NO! But 7 + 4 = 7 + 4. The equation is still true if we add 4 to both sides.

Think of this equation as a balance scale. Solve r + 16 = -7 Think of this equation as a balance scale. r + 16 -7 = Whatever you do to one side has to be done to the other to keep it balanced!

Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

Solve r + 16 = -7 - 16 -16 r = -23 -23 + 16 = -7 Draw “the river” to separate the equation into 2 sides Subtract 16 from both sides Simplify vertically Check your answer by substituting your answer back into the problem

Solve x + 2 = -3 - 2 - 2 x = -5 -5 + 2 = -3 Draw “the river” to separate the equation into 2 sides Subtract 2 from both sides Simplify vertically Check your answer by substituting your answer back into the problem On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

Example x - 6 = 10

Example -25 = x + 13 = x -13 - 13 -38

Example: 13 + y = 20 = y - 13 -13 7

Solve x + 2 = -3 Get the variable by itself. What is your first step? A. Add 2 to both sides B. Subtract 2 from both sides C. Add 3 to both sides D. Subtract 3 from both sides Answer Now

Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 Draw “the river” to separate the equation into 2 sides Add 3 to both sides Simplify vertically Check your answer by substituting your answer back into the problem

4) Solve y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 Draw “the river” to separate the equation into 2 sides Add 3 to both sides Simplify vertically Check your answer by substituting your answer back into the problem

Try these on your own...