Q66. - Algebra 2

Question

Solve each equation. Check your solutions.

66. $\left|\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{7}\right|\mathbf{=}\mathbf{15}$

Step-by-Step Solution

Answer

The solution set of given equation is$\left\{\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{11}\right\}$.

Step 1 – Description of step.

For any real numbers$p$ and $q$, where $q\ge 0$, 

Case 1) if $\left|p\right|=q$ then $p=q$ or 

Case 2) if $\left|p\right|=q$ then$p=-q$

Step 2 – Description of step.

Apply case 1 mentioned in step 2 to $\left|2x+7\right|=15$ and simplify.

$\begin{array}{l}2x+7=15\\ 2x+7-7=15-7\\ \frac{2x}{2}=\frac{8}{2}\\ x=4\end{array}$

Step 3 – Description of step.

Apply case 2 mentioned in step 2 to $\left|2x+7\right|=15$ and simplify.

$\begin{array}{l}2x+7=-15\\ 2x+7-7=-15-7\\ \frac{2x}{2}=\frac{-22}{2}\\ x=-11\end{array}$

Step 4 – Description of step.

To check whether the obtained value of $x$ is the solution of given equation, substitute 4 for $x$ into $\left|2x+7\right|=15$ and simplify.

$\begin{array}{l}\left|2x+7\right|=15\\ \left|2\left(4\right)+7\right|\stackrel{?}{=}15\\ \left|8+7\right|\stackrel{?}{=}15\\ \left|15\right|\stackrel{?}{=}15\\ 15=15\end{array}$

Step 5 – Description of step.

To check whether the obtained value of $x$ is the solution of given equation, substitute $-11$ for $x$ into $\left|2x+7\right|=15$ and simplify.

$\begin{array}{d}\left|2x+7\right|=15\\ \left|2\left(-11\right)+7\right|\stackrel{?}{=}15\\ \left|-22+7\right|\stackrel{?}{=}15\\ \left|-15\right|\stackrel{?}{=}15\\ 15=15\end{array}$

Therefore, the solution set of given equation is