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} (9x)/(9)=(6)/(9) \\ x=(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} (9x)/(9)=(-40)/(9) \\ x=-(40)/(9) \end{gathered}`

The solutions of the equation are

`(2)/(3),-(40)/(9)`