Transcript Document

Multi-Step
Inequalities
TOOLBOX:
Inverse Operations
Addition
Subtraction
Multiplication
Division
What you do to one side of the inequality…
You MUST do to the other
5x + 3x
3(m + 5)
8x
3m + 15
SUMMARY:
Solve and graph
*Read Directions
1) -5m + 16 < 21
- 16
Original Problem
- 16
keep best friend
so get rid of 16 first
-5m < 5
-5
-5
m > -1
Flip!
-2
-1
(3) •
Inverse of mult -5 is Divide -5
Solution
0
2) 4 ≤ x + 1
3
-1
Inverse of +16 is -16
3 ≤ x • (3)
3
Inverse of +1 is -1
Inverse of Divide 3 is Multiply 3
Solution: x ≥ 9
8
9
Original Problem
3 is closest to x…keep best friend
so get rid of 1 first
-1
9≤x
When you multiply or Divide by a negative…
You MUST FLIP the sign
10
We did NOT multiply by a neg on both sides
so… We don’t flip the sign
Solve and graph.
*Read Directions
3) 5n + 3n – n + 5 > 26
7n + 5 > 26
-5
-5
7n > 21
7
7
n>3
1
2
3
4
5
Original Problem
5, 3, and - are closest to n so…
combine the Like Terms (n’s)
Now it is just a two-step inequality
Inverse of +5… -5
Inverse of •7… ___
7
Solution
Solve and graph
4) -3(d – 3) ≥ 18
*Read Directions
Original Problem
# touching ()… Distributive Property
-3d + 9 ≥ 18
-9
-9
Now it is just a two-step inequality
-3 is closest to d…keep best friend
so get rid of 9 first
Inverse of +9… -9
-3d ≥ 9
-3
-3
Inverse of • (-3)… ___
-3
When you multiply or Divide by a negative…
You MUST FLIP the sign
d ≤ -3
Flips!
-4
-3
-2
Solution