Question

Solve the following question. If there are multiple answers, enter each answer separated by a comma. Enter none if there are no solutions. |9x+17|-11=12

Answer 1

The given equation is

$\lvert9x+17\rvert-11=12$

At first, add 11 to both sides

$\begin{gathered} \lvert9x+17\rvert-11+11=12+11 \\ \lvert9x+17\rvert=23 \end{gathered}$

Now, we will have 2 equations

$9x+17=23,9x+17=-23$

We will solve each one

$9x+17=23$

Subtract 17 from both sides

$\begin{gathered} 9x+17-17=23-17 \\ 9x=6 \end{gathered}$

Divide both sides by 9

$\begin{gathered} \frac{9x}{9}=\frac{6}{9} \\ x=\frac{2}{3} \end{gathered}$$9x+17=-23$

Subtract 17 from both sides

$\begin{gathered} 9x+17-17=-23-17 \\ 9x=-40 \end{gathered}$

Divide both sides by 9

$\begin{gathered} \frac{9x}{9}=\frac{-40}{9} \\ x=-\frac{40}{9} \end{gathered}$

The solutions of the equation are

$\frac{2}{3},-\frac{40}{9}$