Question

Which of the graphs below represents the solution set for $|x-3|-4=0$.

Short answer

The correct solution is

Step-by-step solution

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line,without considering direction. The absolute value of a number is never negative.

Step 2- Simplify the expression.

Consider the expression $|x-3|-4=0$.

Add 4 on both sides of the equation as follows:

$\begin{array}{l}|x-3|-4=0\\ |x-3|-4+4=4\\ |x-3|=4\end{array}$

Step 3- Step description.

Apply the absolute rule as follows:

Case 1. When $x-3=4$.

$\begin{array}{l}x-3=4\\ x=4+3\\ x=7\end{array}$

Case 2. When $x-3=-4$

$\begin{array}{l}x-3=-4\\ x=-4+3\\ x=-1\end{array}$

Therefore, the value is $x=-1,7$.

Step 4- Step description.

The correct solution is option (B).