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Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 20 Page 32

Can the absolute value of a number be negative?

Solution:No solution
Number Line:

Practice makes perfect

Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality.

|x-1|+5=2

SubEqn

LHS-5=RHS-5

|x-1|=- 3

An absolute value measures an expression's distance from a midpoint on a number line. Since distance cannot be negative, the absolute value of a number cannot be negative. |x-1|≠ -3 An absolute value cannot be equal to -3, so this absolute value equation has no' solution. Let's graph this.