Question

Simplify. (write each expression without using the absolute value symbol.)

1.|x+3| if x > 5
2. |x+3| if x>2

Answer 1

1.

If x > 5, then the absolute value on |x+3| isn't actually doing anything.

|x+3| = x+3 (without the absolute value) since x+3 is positive for x > 5.

2.

If x > 2, then the absolute value on |x+3| again isn't actually doing anything.

|x+3| = x+3 (without the absolute value) since x+3 is positive for x > 2.

You'd have to be dealing with x-values less than -3 for the absolute value to impact the calculation. Only for x < -3 would "x+3" not be positive and only then does the absolute value change the result.