Download Algebra PPT Lesson 2-8

Objective - To find the opposite of a sum or
difference.
Opposite of a sum
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.
1)  (x  5)
3)  (m  y  2)
x  5
2)  (y  3)
y  3
m  y  2
4)  (a  2b  7)
a  2b  7
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  (8)
2
10  3  5
75
2
a  (b  c)  a  b  c
Distribute the negative!
a  1(b  c)  a  b  c
Subtracting a Quantity
1) -(x + 6)
-x - 6
6) -(3a + 1)
-3a - 1
2) -(2x - 8)
-2x + 16
3) 10 - (4m + 3)
10 - 4m - 3
- 4m + 7
4) 2(x - 5) - (x - 3)
2x - 10 - x + 3
x-7
7) -(-3x + 2y - 7)
+3x - 2y + 7
8) -12 - (3y - 8)
-12 - 3y + 8
- 3y - 4
9) 4(3k - 5) - (2k + 9)
12k - 20 - 2k - 9
10k - 29
Simplify the following.
1) 10 - 4(x - 5) - 8
4) 5x - 4(7x - 9) - 11
5x - 28x + 36 - 11
10 - 4x + 20 - 8
- 23x + 25
- 4x + 22
2) 6 - 2(5 - x) - (3x + 7)
6 - 10 + 2x - 3x - 7
- x - 11
3) 4x - 5[2(6x - 3) - 7]
4x - 5[12x - 6 - 7]
4x - 5[12x - 13]
4x - 60x + 65
-56x + 65
5) 10 + 3(x - 5) - (2x - 9)
10 + 3x - 15 - 2x + 18
x + 13
6) -4[-(x + 5) - 3(x - 6)]
-4[-x + -5 - 3x + 18]
-4[-4x + 13]
16x - 52