Objective - To find the opposite of a sum or difference.

-(x + y) = -x +

-1(x + y) = -1x + -1y

-yOpposite of a sum

-(x - y) = -x +

-1(x - y) = -1x + 1y

yOpposite of a difference

Simplify the following.1) (x 5)

2) (y 3)

3) (m y 2)

4) (a 2b 7) x

y

m y 2

a 2b 7

5

3

Subtracting a Sum or Difference

Judy has $10, owes Sam $3, and owes Talia $5.How much will she have after paying them?

10 (3 5) 10 3 5 10 (8)

2

7 52

a (b c) a b c

a 1(b c) a b c Distribute the negative!

Subtracting a Quantity

1) -(x + 6)

2) -(2x - 8)

3) 10 - (4m + 3)

4) 2(x - 5) - (x - 3)

6) -(3a + 1)

7) -(-3x + 2y - 7)

8) -12 - (3y - 8)

9) 4(3k - 5) - (2k + 9)

-x - 6

-2x + 16

10 - 4m - 3

- 4m + 7

2x - 10 - x + 3 x - 7

-3a - 1

+3x - 2y + 7

-12 - 3y + 8

- 3y - 4

12k - 20 - 2k - 9 10k - 29

Simplify the following.1) 10 - 4(x - 5) - 8

2) 6 - 2(5 - x) - (3x + 7)

3) 4x - 5[2(6x - 3) - 7]

4) 5x - 4(7x - 9) - 11

5) 10 + 3(x - 5) - (2x - 9)

6) -4[-(x + 5) - 3(x - 6)]

10 - 4x + 20 - 8- 4x + 22

6 - 10 + 2x - 3x - 7- x - 11

4x - 5[12x - 6 - 7]4x - 5[12x - 13]4x - 60x + 65

-56x + 65

5x - 28x + 36 - 11- 23x + 25

10 + 3x - 15 - 2x + 18x + 13

-4[-x + -5 - 3x + 18]-4[-4x + 13]

16x - 52