Exercise 16 Page 211

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

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.

To check our solutions, we will substitute them into the equation.

|y|+3=3

Substitute

y= 0

| 0|+3? =3

AbsPos

|0|=0

0+3? =3

AddTerms

Add terms

3=3 ✓

Since the substitution resulted in an identity, y=0 is the correct solution.