Absolute Value Inequalities

| 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

| k - 3 | < -1

• No Solution
• All Real Numbers
• 2 < k < 4
• k < 2  or  k > 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

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

| x + 3 | > 8

• No Solution
• All Real Numbers
• x < -11  or  x > 5
• -5 < x < 11

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

| 3x - 9 | < 3

• x < - 10 or x > - 2
• -10 < x < - 2
• x < 2 or x > 4
• 2 < x < 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

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

| n + 2 | - 3 ≥ -6

• No Solution
• All Real Numbers
• n ≤ -5  or  n ≥ 1
• -5 ≤ n ≤ 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

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

|-9v| < 54

• -6<v<6
• v<-6 or v>6
• v=6 or v=-6
• -6>v<6

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3