Solving Equations by Adding and Subtracting

Think of an equation as a balance scale.

When you solve an equation, your goal is to isolate the variable.

What you do to one side of an equation, you must do to the other side to keep it

the equation balanced.

Golden Rule of Equations

ADDITION and SUBTRACTION “balance” each other

MULTIPLICATION and DIVISION“balance” each other

Addition Property of Equality

You can Add the same number to each side of an equation without changing the

value.

Y - 5 = 13Y - 5 +(5) = 13 + 5

Y = 18

Subtraction Property of Equality

You can SUBTRACT the same number from each side of an equation without

changing the value.

Y + 5 = 13Y + 5 -(5) = 13 - 5

Y = 8

Examples

1.t – 58 = 71

2. x – 6 = -55

3. 114 + m = 249

4. x – 34 = -46

Examples Cont.

5. x + x = 64

6. x – x = 64

7. The sale price of a camera is $119. This is $35 less than the original price. What was the original price?

Division Property of Equality

=3x 18

Examples1. 5b = -235

2. -7h = 35

3. d/4 = 7

Remember: Whatever you do to one side of an equation, you must do to the other!

Be careful: you cannot divide by

zero: Division by ZERO isUNDEFINED