Absolute Value Inequalities

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

• all real numbers

• no solution

• drop the bars

• make 2 cases

• add 3 to both sides

• divide both sides by -3

Is this an "and" or an "or" problem?

• and

• or

• not enough information

• no solution

• and
• or

• Subtract 5 from both sides

• Add 3 to both sides

• Divide both sides by -3

• Drop the bars

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

• -13 ≤ p ≤ 7
• p ≤ -13 or p ≥ 7
• -7 ≤ p ≤ 13
• p ≤ -7 or p ≥ 13