2.6 Solving Absolute Value Inequalities

An absolute value inequality is

• an inequality that contains an absolute value expression
• impossible to solve
• an equation that contains an absolute value expression
• always going to have two solutions

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| x + 3 | ≤ 2

• No Solution
• All Real Numbers
• -5 ≤ x ≤ -1
• 1 ≤ x ≤ 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

| x | ≤ 3.5

• No Solution
• All Real Numbers
• -3.5 ≤ x ≤ 3.5
• x ≤ -3.5  or  x ≥ 3.5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

| 3c - 5 | < -2

• No Solution
• All Real Numbers
• 1 < c < ⁷/₃
• c < 1  or  c > ⁷/₃

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| x + 1 | ≥ 3

• No Solution
• All Real Numbers
• x ≤ -4  or  x ≥ 2
• -4 ≤ x ≤ 2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

| 12 + w | ≥ -5

• No Solution
• All Real Numbers
• w ≤ -17  or  w ≥ -7
• -17 ≤ w ≤ -7

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

3 | 2t - 3 | - 5 > 16

• No Solution
• All Real Numbers
• t < -2  or  t > 5
• -2 < t < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

3 | d + 1 | - 7 ≥ -1

• No Solution
• All Real Numbers
• d ≤ -3  or  d ≥ 1
• -1 < d < 3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3