Solving Absolute Value Inequalities
Definition:
x  a means x  a or x  a
-a
0
a
Definition:
x  a means x  a and x  a
-a
0
a
Keys to Solving Absolute Value Inequalities
GreatOR
Less ThAND
x a
x a
xa
OR
x  a
xa
AND
x  a
2
x3  2
3
2
x3 2
3
OR
GreatOR
2
x  3  2
3
2

3 x  3  3 2
3

2

3  x  3   3  2 
3

2x  9  6
2 x  9  6
2 x  3
3
x
2
2 x  15
OR
15
x
2
5  2x  4
5  2x  4
AND
2 x   1
1
x
2
Less ThAND
5  2 x  4
2 x  9
AND
9
x
2
Your Turn…
Make two cases.
Solve the two
cases
independently.
Solve | 2x + 3 | < 6.
2 x  3  6 AND 2 x  3  6
2 x  3 AND
2 x  9
3
9
x
AND
x
2
2
Your Turn…
Make two cases.
Solve the two
cases
independently.
Solve | 2x – 3 | > 5.
2 x  3  5 OR 2 x  3  5
2 x  8 OR
2 x  2
x  4 OR
x  1
Challenges…
HINT:
Think
midpoint
and
distance.
Find the absolute-value
inequality statement
that corresponds to the
inequality
–2 < x < 4.
Find the absolute-value
inequality statement
that corresponds to the
inequalities
x < 19 or x > 24.
More Help???
http://www.purplemath.com/modules/absineq.htm
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name and
password.
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http://regentsprep.org/Regents/mathb/7D
8/absinequal.htm