Question

Solve each equation. Then graph the solution set.

$\left|x-6\right|=11$

Short answer

The Solution set is $\{-5,17\}$.

Step-by-step solution

Step 1. Case when the modulus expression is positive.

The absolute value or modulus of a real number x, denoted $\left|x\right|$,it is the non-negative value of $x$without regard to its sign.

$\left|x\right|=x$if $x$is positive,

$\left|x\right|=-x$if $x$is negative,

$\left|0\right|=0$.

For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.

We are given the expression$|x-6|=11$ assuming a positive value for the modulus expression we get:

role="math" localid="1643044816534" $\begin{array}{l}x-6=11\\ x-6+6=11+6\left[add6bothsides\right]\\ x=17\end{array}$

Thus$x=17$ is one of the solutions.

Step 2. Case when the modulus expression is negative.

$\begin{array}{l}x-6=-11\\ x-6+6=-11+6\left[add6bothsides\right]\\ x=-5\end{array}$

Thus$x=-5$ is one of the solutions.

Step 3. Graphing the solution set.

The solution set is $\{-5,17\}$, we graph these values on the number line as shown below: