1. Sec. 1-5: Absolute Value Equations & Inequalities.
9/7/17

2. Steps to Solving Absolute Value Probs
Get the absolute value symbol BY ITSELF!
** Remember NOT to distribute through absolute value!
Determine if it is an “AND” or “OR” problem. Write the 2 problems. (< means AND; = or > means OR)
** Remember to reverse the signs on the 2nd problem, including the inequality sign.
Solve each problem separately.
Check your solutions!! You may have extraneous solution(s)!

3. Now, CHECK TO MAKE SURE BOTH ANSWERS WORK!!!
Solve: |x + 4| = 2x – 6
It is an OR problem. Write your compound equation.
x + 4 = 2x – or x + 4 = -2x + 6
-x = or x = 2
x = or x = 2/3
Now, CHECK TO MAKE SURE BOTH
ANSWERS WORK!!!

4. NOW CHECK THE SOLUTIONS! They work. Graph on a number line.
y – 3 > OR y - 3 < -12
y > 15 OR y < -9
NOW CHECK THE SOLUTIONS!
They work. Graph on a number line.

5. |2m + 4| < 10
2m + 4 < AND 2m + 4 > -10
2m < 6 AND m > -14
m < 3 AND m > -7
NOW CHECK THE SOLUTIONS!
They work. Graph on a number line.
The answer is:
-7 < m < 3

6. Absolute Value Recap <, < mean AND >, >, and = mean OR
Absolute value probs must be written as two separate probs..
1. Positive case written “as is”
2. Negative case; Switch inequality symbol!

7. My wish, nay, my command is for you to start working
Pg 36 #13 –18, 24 – 26