Question

Solve. If there is more than one solution, separate them with a comma. − 6 + 4 | − 6 x + 9 | = − 34

Answer 1

Given

`-6+4\left|-6x+9\right|=-34`

Solve for x

`\begin{gathered} -6+4\lvert-6x+9\rvert+6=-34+6 \\ 4\lvert-6x+9\rvert=-28 \end{gathered}`

Divide by 4 to both sides

`\begin{gathered} (4|-6x+9|)/(4)=(-28)/(4) \\ |-6x+9|=-7 \end{gathered}`

The absolute value cannot be less than zero. Therefore, the equation has no solution.

Answer:

no solution for x ∈ R