1. Solving Compound Inequalities And
Rule 1: Whatever you do to one section you have to do to the other two.
Rule 2: Remember all of the rules for solving equations.
Rule 3: If you multiply/divide by a negative number you must change the direction of the inequality symbol.

2. -2 < x < 3 AND -2 < 3x + 4 < 13 -4 -4 -4 -6 < 3x < 9
-6 < 3x < 9
-2 < x < 3

3. Solving Compound Inequalities OR
Rule 1: Work each piece separately.
Rule 2: Remember all of the rules for solving equations.
Rule 3: If you multiply/divide by a negative number you must change the direction of the inequality symbol.

4. OR 2x + 3 < or 4x – 7 > 9
2x < 2 or 4x > 16
x < or x > 4

5. Solving Absolute Value Equations and Inequalities
Sect 1.7
Solving Absolute Value Equations and Inequalities

6. The result of an absolute value is always positive.
of a number x, written |x|, is the distance a number is form 0 on the number line.
The result of an absolute value is always positive.

7. Examples:
|-5| = 5
|5| = 5
Your turn to try:
|-2| = 2
|2| = 2

8. To Solve an absolute value equation of the form |x| = c, where c > 0, you must consider 2 answers:
x = c or x = -c

9. Examples: |x| = 5 x = 5 or x = -5 |x| = -2 -2 No solution
Remember: an Absolute Value result is always positive

10. Solving Absolute Value Equations
|ax + b| = c, where c > 0
is equivalent to the compound statement:
ax + b = c or ax + b = -c

11. Steps for solving Absolute value equations:
Step 1: Rewrite problem as the compound or statement
Step 2: Solve each new equation separately
Step 3: Write the answer

12. Examples:
|2x – 5| = 9
Step 1: Rewrite
2x – 5 = or 2x – 5 = -9

13. Step 2: Solve individually
2x – 5 = or 2x – 5 = -9
2x = or x =
Step 3: Write answer
x = or x = -2

14. Your Turn Again: |3x + 8| = 20 3x + 8 = 20 or 3x + 8 = -20 -8 -8 -8 -8
3x = x = -28
x = or x = -28/3

15. Solving Absolute Value Inequalities
|ax + b| < c, where c > 0
is equivalent to the compound statement:
-c < ax + b < c

16. Solving Absolute Value Inequalities
|ax + b| > c, where c > 0
is equivalent to the compound statement:
ax + b > c or ax + b < -c

17. Recap:
Absolute value equations and inequalities are both solved with compound statements.
>, ≥, =
are all or statements
<, ≤
are and statements

18. Your turn once again: -9 < x < 2 |2x + 7| < 11
-18 < 2x < 4
-9 < x < 2

19. Now try this one: x ≥ 10/3 or x ≤ -2 |3x - 2| ≥ 8
3x ≥ or 3x ≤ -6
x ≥ 10/3 or x ≤ -2

20. Classwork – Journal entry –
What are the steps for solving compound inequalities and absolute values?
Pg , 2, 4, 7, 10, 13
Homework –
Pg , 40, 43, 44
Pg 53 – every 3rd, 47-50