1. Objective - To find the opposite of a sum or difference.
Opposite of a difference
-(x + y)
= -x + -y
-(x - y)
= -x + y
-1(x + y)
= -1x +
-1y
-1(x - y)
= -1x + 1y
Simplify the following.

2. Subtracting a Sum or Difference
Judy has $10, owes Sam $3, and owes Talia $5.
How much will she have after paying them?
Distribute the negative!

3. Subtracting a Quantity
1) -(x + 6)
6) -(3a + 1)
-x - 6
-3a - 1
2) -(2x - 8)
7) -(-3x + 2y - 7)
-2x + 16
+3x - 2y + 7
3) (4m + 3)
8) (3y - 8)
10 - 4m - 3
y + 8
- 4m + 7
- 3y - 4
4) 2(x - 5) - (x - 3)
9) 4(3k - 5) - (2k + 9)
2x x + 3
12k k - 9
x - 7
10k - 29

4. Simplify the following.
1) (x - 5) - 8
4) 5x - 4(7x - 9) - 11
10 - 4x
5x - 28x
- 4x + 22
- 23x + 25
2) 6 - 2(5 - x) - (3x + 7)
5) (x - 5) - (2x - 9)
x - 3x - 7
10 + 3x x + 18
- x - 11
x + 13
3) 4x - 5[2(6x - 3) - 7]
6) -4[-(x + 5) - 3(x - 6)]
4x - 5[12x ]
-4[-x x + 18]
4x - 5[12x - 13]
-4[-4x + 13]
4x - 60x + 65
16x - 52
-56x + 65