Solving Inequalities and Absolute Value Equations

|2x| ≤ 14; Is this an AND or an OR?

• AND

• OR

Solve the following compound inequality:

−8 < 2(x + 4) or −3x + 4 > x − 4

• No solutions

• x < −8 or x < 2

• x > −8 or x < 2

• x < −8 and x < 2

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

Solve:

2x² + 5x ≥ 12 , then find the interval notation of the inequality.

• [-4, 1.5]

• (−∞, -4) U (1.5, ∞)

• (−∞, -4] U [1.5, ∞)

• no solution

Solve:
|x + 3| > - 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

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

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

What is the solution to the absolute value equation 2|4x - 1| = 6?

• {-1/2, 1}

• {-4, 8}

• {-1}

• No Solution

What is the solution to the inequality 3|2x - 4| ≥ -9?

• ℝ

• (-∞, 9) ∪ (9, ∞)

• No Solution

• { -1 }

What is the solution to the inequality -4|3x - 1| ≥ 8?

• ℝ

• (-∞, 9) ∪ (9, ∞)

• No Solution

• { -1 }

What is the solution to the inequality -5|2x + 2| - 3 ≥ -3?

• ℝ

• (-∞, 9) ∪ (9, ∞)

• No Solution

• { -1 }