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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 16 Page 211

How many cases do you have after you remove the absolute value?

Solutions: y=0
Graph:

Practice makes perfect

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

|y|+3=3

SubEqn

LHS-3=RHS-3

|y|+3-3=3-3

AddTerms

Add terms

|y|=0

An absolute value measures an expression's distance from a midpoint on a number line.

|y|= 0 The equation means that the distance between y and 0 is 0, either in the positive direction or the negative direction. This can be expressed as an equation equivalent to the absolute value equation. |y|= 0 ⇒ y= 0 In this case, our absolute value expression is only the variable y, so our equivalent equation does not need any more simplifying. Now let's graph this solutions on a number line.