Solving Inequalities Absolute Value Equations and Inequalities

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5

• x ≤ -2 OR x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x < 5

Write an inequality for Graph 4.

• -2 < x < 5

• x < -2 or x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x ≤ 5

Which compound inequality involves <, ≤ when solving absolute value inequalities?

• and

• or

Which compound inequality involves >,≥ when solving absolute value inequalities?

• and

• or

| x | ≤ 3.5

• No Solution

• All Real Numbers

• -3.5 ≤ x ≤ 3.5

• x ≤ -3.5  or  x ≥ 3.5

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

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

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

Solve | 3x - 6 | - 9 = -3

• No Solution

• x = 0 or x = 4

• x = 2 or x = -2

• x = -4 or x = 4

What is the range of the absolute value function?

• (-infinity, infinity)

• [3, infinity)

• [0, infinity)

• (-infinity, 3]

What is the first step? 

• Get absolute value alone by subtracting 5 from both sides

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

• Split into two equations