1. Inequality Symbols Topic: Solving Inequalities
Name:
Date:
Period:
Topic: Solving Inequalities
Essential Question: What is the correlation between solving equations and solving inequalities?
Warm-up:
Name the following inequality signs:
Inequality Symbols
Less than
Not equal to
Less than or equal to
Greater than or equal to
Greater than

2. Vocabulary:
An inequality is like an equation, but instead of an equal sign (=) it has one of these signs:

3. Solving Inequalities by
Adding or Subtracting

4. Solving the Inequality
w + 5 < 8
Note:
We will use the same steps that we did with equations, if a number is added to the variable, we subtract the same number to both sides.

5. All numbers less than 3 are solutions to this problem!
Answer
w + 5 < 8
w < 8 -5
w + 0 < 3
w < 3
All numbers less than 3 are solutions to this problem!

6. Now you try it! 8 + r ≥ -2 7 > x – 5 x - 2 > -2 4 + y ≤ 1

7. Answers to Practice Problems:
x - 2 > -2
4 + y ≤ 1
x >
r ≥ -2 -8
y ≤ 1 - 4
x + 0 > 0
y + 0 ≤ -3
r + 0 ≥ -10
x > 0
y ≤ -3
w ≥ -10
All numbers from -10 and up (including -10) make this problem true!
All numbers from -3 down (including -3) make this problem true!
All numbers greater than 0 make this problem true!

8. Answers to Practice Problems:
x + 2 ≤ 3
x - 5 > 7
x ≤ 7 - 2
x – > 7 + 5
x + 0 ≤ 5
x + 0 > 12
x ≤ 5
x > 12 12 5

9. What do these means?
x < 5
x ≤ 3
x > 4
x ≥ 2

10. How to graph the solutions
> Graph any number greater than. . .
open circle, line to the right
< Graph any number less than. . .
open circle, line to the left
Graph any number greater than or equal to. . .
closed circle, line to the right
Graph any number less than or equal to. . .
closed circle, line to the left
x > 4
x < 5
x ≥ 2
x ≤ 3

11. Multiplying or Dividing
Solving Inequalities by
Multiplying or Dividing

12. Solving the Inequality
< - 2
15b < 60

13. Answers x < - 8 15b < 60 15b < 60 b < 4 15 15 < - 2

14. But wait there is one special case:
That was easy!!!
But wait there is one special case:
Sometimes you may have to reverse the direction of the inequality sign!!
That only happens when you multiply or divide both sides of the inequality by a negative number.

15. Solving the Inequality
- 4r > 16

16. ( ( ( ( Answers - 4r > 16 - 4r > 16 r < - 4 - 4 - 4
m < - 10
- 4r > 16
- 4r > 16
r < - 4
- 4
- 4

17. Solving Multi-Step
Inequalities

18. Solving multi-step inequalities is like solving multi-step equations.
If you can solve
you can solve

19. Remember:

20. Which graph shows the solution to 2x - 10 ≥ 4?

21. Now you try it!
Page 181 (1 – 4, 8, 16, 20)
1) (x + 4) - 5(x - 1) < 5
-2x + 6 ≥ 3x – 4
3 (t + 1) – 4t ≥ - 5
5m - 8 > 12
-5x – 9 < 26
V.I.I.
Anytime you multiply or divide both sides of an inequality by a negative number, you need to reverse the sign.

22. Brief Review of Inequalities
Wrap-Up:
Brief Review of Inequalities
Add/subtract the same number on each side of an inequality
Multiply/divide by the same positive number on each side of an inequality
If you multiply or divide by a negative number, you MUST flip the inequality sign!
Home-Learning:
Page 175 (34), Page 176 (70),
Page 181 (12, 21, 24), Page 189 (2, 4),
Page 190 (20), Page 192 (59, 60)