Solving/Interpreting Linear Inequalities in One Variable Absolute Value

Solve the absolute value inequality: |2x - 1| ≥ 5.

• x ≤ -2 or x ≥ 3

• x ≤ -3 or x ≥ 2

• x ≤ -1 or x ≥ 4

• x ≤ -2 or x ≥ 3

Solve the absolute value inequality: |2x - 3| < 5.

• x < 2/3 or x > 2/3

• x < 1/2 or x > 1/2

• x < 3/2 or x > 3/2

• x < -3/2 or x > 3/2

If a is a solution of ∣x + 3 ∣ ≥ 8, then a is also a solution of x + 3 ≥ −8. (a)  

• false

• true

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

Solve for v:

|4v + 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

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

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve the absolute value inequality: |2x + 5| < 3.

• -5/2 < x < -1/2

• -5/2 < x < 0

• -5/2 < x < 1/2

• -5/2 < x < -1/2

|2x| ≤ 14; Is this an AND or an OR?

• AND

• OR

What is the first step?

• Get the absolute value alone by dividing both sides by 5

• Drop the absolute value bars and add 7 and 5 together

• Get the absolute value alone by subtracting 5 from both sides