Question

Solve each equation. (Lesson 2-5)

$\left|x+5\right|=-8$

Short answer

The equation does not have a valid solution or the solution is the null set.

Step-by-step solution

Step 1. Use the definition of the absolute value function.

The absolute value or modulus of a real number xdenoted |x| is the non-negative value of x without regard to its sign.

Absolute value refers to a point's distance from zero or origin on the number line, regardless of the direction.

Step 2. Identify the expression having commutative property.

We are given the expressions: $\left|x+5\right|=-8$

Since an absolute function value can never be negative we have -8 on the right hand side which is not possible.

Therefore this expression does not have a valid solution.

Hence, the solution set will be an empty set for the given expression.