# #5 - Absolute Value Equations and Inequalities

```Name_____________________
#5 - Absolute Value Equations and Inequalities
Equations
Goal: Solve for “x”.
How To Do:
1. Isolate the absolute value expression.
2. Remove the absolute value symbols.
3. Rewrite as 2 equations. (one equals
positive number &amp; one equals negative
number)
4. Solve each equation for “x”.
1. 3n  5  7
5. 5 2 x  4  10
2. 4  2 x  10
6. 3x  6  18
3. 11  5  3x  7
7. 2 x  7  9  21
4. 2  x  5  6
Inequalities
Steps:
 To solve | ax+b |&lt;c, solve the compound inequality –c&lt;ax+b&lt;c (think of this as a
sANDwich inequality &amp; that the solution set will be the intersection of the solution
sets of ax+b&gt;-c AND ax+b&lt;c)
-c
0
c
 To solve | ax+b |&gt;c, solve the compound inequalities: ax+b&lt;-c OR ax+b&gt;c.
(think of this – greater than means mORe than &amp; the solution set will be
the union of the solution sets of ax+b&lt;-c &amp; ax+b&gt;c)
-c
0
c
Solve each absolute value inequality and graph on a number line.
1. |4x – 3| &lt; 5
3. -3 2 x  6  1  8
2. 4 + |2x + 6| &lt; 15
4.
2  3 2 x  1  20
2
3
```