Solving Two-Step Absolute Value Equations

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Order the numbers from least to greatest.
-2, I8I, 5, I-10I, 6

• -2, I8I, 5, I-10I, 6
• -10, -2, 5, 6, 8
• -2, 5, 6, 8, 10
• I-10I, -2, 5, 6. I8I

|x-3|=40

• x = 43, x = -37

• x = 43, x = -43

• x = -43, x = 37

• x = 43

|x+7|=12

• x = -5, x = 19

• x = 5, x = -19

• x = 5, x = -5

• x = 12, x = -7

|-2 - 4n| = 34

• n = -9, n = 8
• n = 9, n = 8
• n = -9
• n = 8

|2a - 10| = 6

• a = 8, a = 5
• a = 2
• a = 8
• a = 8, a = 2

8|-2x + 4| = 96

• x = -4, x = 8
• x = -4
• x = -4, x = -8
• x = 4, x = 8

An absolute value equation is

• an equation that contains an absolute value expression
• always going to have two solutions
• always going to have one solution
• impossible to solve

| 2x - 1 | = -4

• x = ¹/₂ and x = -4
• No Solution
• x = ^-3/₂ and x = ⁵/₂
• x = ³/₂ and x = ^-5/₂

| 3x - 6 | - 9 = -3

• No Solution
• x = 0 and x = 4
• x = 2 and x = -2
• x = -4 and x = 4