Objective - To solve equations using the properties of equality.

Addition Property of EqualityIf a = b, then a + c = b + c

orGiven a = b

and c = cthen a + c = b + c

Subtraction Property of EqualityIf a = b, then a - c = b - c

orGiven a = b

and c = cthen a - c = b - c

=x + 3 7- 3 Heavier

=x 7Heavier

=x7 Heavier

=x

7 Heavier

=x

7 Heavier

=x + 3 7- 3 - 3

=x 4

Algebraically,

x + 3 = 7-3 -3x = 4

x + 3 = 7

x = 4x + 3 - 3 = 7 - 3

1) Goal: Isolate the variable on one side of the equation.

2) Always perform the same operation toboth sides of an equation.

3) To undo an operation, perform its opposite operation to both sides of the equation.

Solve the equations below.

1) x + 3 = 10- 3 - 3

x = 7

2) y - 8 = 11+8 +8

y = 19

3) n + 5 = 11- 5 - 5

n = 6

4) 13 = x + 5- 5 - 5

8 = x

5) 12 = n - 3+3 +315 = n

6) 11 + 3 = k

14 = k

Translate the sentence into an equation and solve.

1) The sum of k and 13 is 28.

2) Five is the difference of t and 4.

k + 13 = 28- 13 - 13

k = 15

5 = t - 4+4 +4

9 = t

Multiplication Property of Equality

If a = b, then a c = b c.

orxIf n,m

xthen nm

or x mn.

m m

Solve.

1)

2)

3)

4)

x 43

x3 4 33

x 12

y16

2

y2 16 2

2

y 32

m 105

m5 10 55

m 50

k 74

k4 7 44

k 28

Division Property of Equality

or

If x m n, then

nor x .m

If a b, then a c b c.

x m n m m

Solve.

1)

2)

3)

4)

5x 205x 20

x 45 5

36 3y36 3y

12 y3 3

24 8t24 8t

3 t8 8

4k 184k 18

18k4

4 4

92

1or 42

Solve.

1)

2)

3)

4)

4x 444x 44

x 114 4

26 2y26 2y

13 y2 2

x 33.2

x3.2 5 3.23.2

x 16

d 4.23

d3 4.2 33

d 12.6