Do Now: Solve, graph, and write your
answer in interval notation.

CAUTION… you must THINK through your
final answer!!!

1) a + 2 > -2 or a – 8 > 1

2) b – 3 > 2 and b + 3 < 4
Solving Absolute Value
Inequalities
Section: 1-6
Page 40 in your textbook
Solving an Absolute Value Inequality
●
Step 1: Rewrite the inequality as a conjunction or a
disjunction.
● If you have a  or  you are working with a
conjunction or an ‘and’ statement.
Remember: “Less thand”
● If you have a  or  you are working with a
disjunction or an ‘or’ statement.
Remember: “Greator”
●
●
Step 2: In the second equation you must negate the right
hand side and reverse the direction of the inequality sign.
Step 3: Solve as a compound inequality.
Example 1:
●
●
●
●
●
|2x + 1| > 7
2x + 1 > 7 or 2x + 1 >7
This is an ‘or’ statement.
(Greator). Rewrite.
2x + 1 >7 or 2x + 1 <-7
In the 2nd inequality, reverse the
inequality sign and negate the
right side value.
x > 3 or
Solve each inequality.
x < -4
Graph the solution.
-4
(-inf., -4) U (3, +inf.)
3
Write the solution in interval
notation.
Example 2:
●
This is an ‘and’ statement.
(Less thand).
|x -5|< 3
●
x -5< 3 and x -5< 3
x -5< 3 and x -5> -3
●
x < 8 and x > 2
●
Rewrite.
In the 2nd inequality, reverse the inequality
sign and negate the right side value.
Solve each inequality.
Graph the solution.
2
●
(2, 8)
8
Write the solution in interval notation.
Example 3:
●
|x |≥ -2
●
x ≥ -2 or x ≤ 2


-3 -2
-1 0
1
2
3
Solution: All Real Numbers
( -inf., +inf.)



This is an ‘or’
statement. (Greator).
Rewrite.
In the 2nd inequality,
reverse the inequality
sign and negate the
right side value.
Solve each inequality.
Graph the solution.
Write the solution in
interval notation.
Example 4:
●
|2x| < -4


2x < -4 and 2x > 4


x < -2 and x > 2

In the 2nd inequality, reverse the
inequality sign and negate the right
side value.

Solve each inequality.

Graph the solution.

Write the solution in interval
notation.
-3 -2 -1 0 1 2 3

NO SOLUTION!!
This is an ‘and’ statement.
(Less thand).
Rewrite.
Solve and Graph
● 1)
|y – 3| > 1
● 2)
|p + 2| < 6
● 3)
| g | - 2 < -4