Question

Solve and graph.Let f(x) = |4x-9|. Find all x values for which f(x) s 14.

Answer 1

When dealing with an absolute value, there are two cases that must be analyzed.

Case 1: 4x-9 > 0

Then:

`|4x-9|=4x-9`

Solving the equation for x:

`\begin{gathered} |4x-9|=14 \\ \Rightarrow4x-9=14 \\ \Rightarrow4x=14+9 \\ \Rightarrow4x=23 \\ \Rightarrow x=(23)/(4) \end{gathered}`

Case 2: 4x-9 < 0

Then:

`|4x-9|=-(4x-9)`

Soving the equation for x:

`\begin{gathered} |4x-9|=14 \\ \Rightarrow-(4x-9)=14 \\ \Rightarrow-4x+9=14 \\ \Rightarrow-4x=14-9 \\ \Rightarrow-4x=5 \\ \Rightarrow x=-(5)/(4) \end{gathered}`

The graph of the function f(x)=|4x-9| is:

Therefore, the solution set is:

`\begin{gathered} x_1=(23)/(4) \\ x_2=-(5)/(4) \end{gathered}`