Absolute Value Algebra

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5 ... 1 ≤ x ≤ 5

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5

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

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

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

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

∣ 2x + 9 ∣ = 15

• x = 3 

• x = 3
  x = -6

• x = 3
  x = -12

• x = 6
  x = -12

Absolute value is . . .

• The opposite of the number inside the brackets

• The distance away from zero

• Making positive numbers negative

• Both positive and negative

What is the correct first step?

• divide both sides by 10

• multiply both sides by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and" or a between statement