ABSOLUTE VALUE INEQUALITIES. Just like absolute value equations, inequalities will have two solutions: |3x - 2| ≤ 7 3x – 2 ≤ 7 +2 +2 3x ≤ 9 x ≤ 3 -5/3.

ABSOLUTE VALUE INEQUALITIES

ABSOLUTE VALUE INEQUALITIES

Just like absolute value equations,

inequalities will have two solutions: |3x -

2| ≤ 7 3x – 2 ≤ 7 +2 +2 3x ≤ 9 x ≤ 3

-5/3 ≤ x ≤ 3[ -5/3, 3 ]

-7 ≤ 3x – 2+2 +2 -5 ≤ 3x -5/3 ≤ x

-7≤ 3x – 2 ≤ 7

ABSOLUTE VALUE INEQUALITIES

Try again:

|2x + 1| < 11

-11 < 2x +1

AND

-12 < 2x

-6 < x

2x +1 < 11

2x < 10

x < 5

-6 < x < 5 ( -6, 5 )

ABSOLUTE VALUE INEQUALITIES

If the sign is less than, the answer is written as

one statement.• |2x + 1| < 11

• -6 < x < 5 (-6, 5)

If the sign is greater than, the answer must be

written as two statements.• See the next problem.

ABSOLUTE VALUE INEQUALITIES

|1 – 2x| > 5

1 – 2x > 5

-1 -1

-2x > 4

x < -2

OR 1 – 2x < -5

-1 -1

-2x < -6

x > 3

x < -2 or x > 3(-∞, -2) U ( 3, ∞)

ABSOLUTE VALUE INEQUALITIES

Practice these:

|2x - 5| < 6

|3x + 6| ≤ 3

|x - 5| > 4

|2x + 5|≥ 8