Absolute Value Equations/Inequalities

How many solutions does this equation have?

∣ 2x + 9 ∣ = 15

• none 

• one

• two

• infinite

Solve for x.

∣ 2x + 9 ∣ = 15

• x = 3 only

• x = 3
  x = -6
• x = 3
  x = -12
• x = 6
  x = -12

How many solutions does this equation have?

∣ x + 9 ∣ = -5

• none 

• one

• two

• infinite

Solve for x.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

How many solutions does this equation have?

∣ x - 3 ∣ = 0

• none 

• one

• two

• infinite

Solve for x.

| x – 3 |= 0

• 3
• -3
• {-3, 3}
• no solution

Solve for x
l x−6 l + 4 = 10

• x = 12 and x = 0
• x = 3 and x = -3
• x = -12 and x = 0
• No Solution

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

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

• and

• or

Solve for x.

| x + 3 | ≤ 2

• No Solution
• 1 ≤ x ≤ 5