Main Events:
• Check:
Test Chapter 1
Wednesday
p. 44 # 5-50(x5), 52
Algebra 2
Warm-up: 9/30/2021
Solve and graph.
1.  2c  7  1
2.  9  w  2  5
3. 7 x  1  x  11 or  11x  33
4. 3 y  5  2 y  1  y  1
5.  2  5 z  7 and  2  5 z  7
Lesson
• Quiz 1.1-1.4(was Friday)
• Review special cases with compound
inequalities.
• Classwork Puzzle D-27
• Powerpoint 1.7 with practice
Section 1.7
Objective: Solve and graph
absolute value equations and
inequalities.
Solve the absolute value
equation:
x 8
x 8
x  8
or
-8
0
8
x  5  10
x  5  10
5 5
x  5  10
or
5
5
x  5
x  15
-5
0
5
10
15
Absolute Value Equations
and Inequalities
To solve absolute value equations, recall that absolute
value means “distance away from zero”.
Just watch
Solve |x + 3| = 5
This means that x + 3 is 5 units away from 0, so there are
two possibilities:
x+3=5
–3 –3
x
= 2
or
x + 3 = –5
–3 –3
or
x = –8
Solve and graph
• Ex 1
a) 2 x  3  7
b) 3x  4  10
c) 13  5 x  2
Check your answer for extraneous solutions.
EX 2 Isolate the absolute value first:
x  1  10  12
10  10
x  1  22
x 1  22
1 1
x  21
or
Begin by
adding 10
to both
sides.
x 1  22
1
1
x  23
What about inequalities?
Example: Solve |x| < 3
This means that the distance on number line must be less
than or equal to 3.
x < 3 and
x > –3
–3 < x < 3
-3
0
3
: Solve |x | > 3
This means that the distance on number line is greater than or
equal to 3.
x > 3 or x < –3
-3
0
3
EX 3 Solve: |x – 3| < 5
“less than”-----And
x–3 < 5
+3 +3
x
< 8
and
and
–2 < x < 8
x – 3 > –5
+3 +3
x > –2
EX 4 Solve: |2x – 8| >4
“great-or than”-----OR
2x – 8 < -4
+8
OR
+8
2x < 4
x
<
2x – 8 > 4
+8 +8
2x > 12
2
OR
x
> 6
Solve each of the following:
Practice 1.7
1.) 2 x  3 5
2.) 3x  4  10
3.) 3x  4  8
4.) 6  2 x 14
Classwork
p. 1010 # 33-53 odd
Homework…
p. 55 # 9-11, 28-30, 35, 38, 56, 61
Closure-• An absolute value equation can have
0, 1, or 2 solutions.
Determine the
number of solutions for each equation?
2 x  5  3x
3x  2  13
x  7  10