Solving absolute 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

| 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

| 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

| 2w - 1 | < 11

• No Solution
• All Real Numbers
• -5 < w < 6
• -6 < w < 5

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

| 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

What is the correct first step?

• divide by 10
• multiply by 10
• make it two inequalities with an "or"
• make it two inequalities with and "and

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| 2x + 12 | < 8
Which is the correct first step?

• 2x + 12 < 8 and 2x+12 >-8
• 2x + 12 < 8 or 2x+12 >-8
• 2x + 12 < 8 and 2x+12 <-8
• 2x + 12 < 8 or 2x+12 >-8

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3