1. 1.6 Solving Linear Inequalities

2. Linear Inequality
A linear inequality is an equation but instead of an = there is an inequality sign.
Ex: 2x + 7 > 3
-3 – 6x ≤ 12

3. Greater than or equal to
Inequality Symbols
Less than
Not equal to
Less than or equal to
Greater than
Greater than or equal to

4. Remember…
If you multiply or divide by a negative number, you MUST flip the inequality sign!

5. Solve the inequality.
2x – 3 < 8

6. Graphing Linear Inequalities
Remember:
< and > signs will have an open dot o
and signs will have a closed dot
graph of graph of 4 5 6 7 -3 -2 -1

7. Solve the inequality. Then graph the solution.
-8x + 12 < -4

8. Solve the inequality. Then graph the solution.
41< 5 – 12x -5 -4 -3 -2 -1 1 2

9. Solve the inequality.
3x + 12 > 5x -2

10. Compound Inequality An inequality joined by “and” or “or”. Examples
think between think outside

11. Solve & graph.
-6x + 9 < 3 or -3x - 8 > 13
Think outside -7 1

12. Solve & graph.
15 < -3x - 6 and -3x - 6 < 12
Think between!

13. Solve & graph.
-9 < t+4 < 10
Think between!
-13 6

14. Solve & graph.
-6 < 4t - 2 < 14

15. Absolute Value Equations and Inequalities

16. Absolute Value
Absolute value of a number is its distance from zero on a number line.
2 units -2 2 1 -1 3

17. Example
Solve

18. Example
Solve

19. Example
Solve:

20. Example: Isolate the absolute value expression FIRST
Solve

21. Example
Solve

22. Solving Absolute Value Inequalities
Step 1: Rewrite the inequality as a conjunction or a disjunction.
If you have a you are working with a conjunction or an ‘and’ statement.
Remember: “Less thand”
If you have a you are working with a disjunction or an ‘or’ statement.
Remember: “Greator”
Step 2: In the second equation you must negate the right hand side and flip the inequality sign.
Step 3: Solve as a compound inequality.

23. Example : Solve then graph

24. Example : Solve then graph

25. Example: Solve then graph

26. Example: Solve then graph