Absolute Value Inequalities

Solve:
|x + 3| > - 8

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

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve:
|x + 4| - 8 > 2

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

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve.
|p + 3| ≥ 10

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

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3
• c < -5 1/3  or c > 2 2/3
• c < 5 1/3 or c > -2 2/3
• -5 1/3 < c < 2 2/3

Tags

CCSS.HSA.REI.B.3

Solve.
|4k + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5
• -4.5 ≤ v ≤ -1.4
• -1.5 ≤ v ≤ 4.5
• v ≤ -1.5 or v ≥ 4.5

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve.
6 - 2|m -3| > -4

• -8 < m < 2
• m < -8 or m > 2
• m < -2 or m > 8
• -2 < m < 8

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Which compound inequality involves <, ≤ when solving absolute value inequalities?

• and

• or

What kind of compound inequality is this?

• AND compound inequality
• OR compound inequality

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve for r.

• r ≥ -38 and r ≤ 32
• r > -38 and r < 32
• r ≥ -38 or r ≤ 32
• r > -38 or r < 32

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3