Question

|4x - 6| < 6Group of answer choices0 < x < 3x > 3 or x < 0x < 3-3 < x < 0

Answer 1

We have the following inequality:

`|4x-6|<6`

Applying the properties of absolute values we have that:

`\begin{gathered} -6<4x-6<6 \\ \end{gathered}`

Which can be expressed as

`4x-6>-6\text{ and }4x-6<6`

We solve separately and mix the intervals:

`\begin{gathered} 4x-6>-6 \\ x>(-6+6)/(4) \\ x>0 \end{gathered}`
`\begin{gathered} 4x-6<6 \\ x<(6+6)/(4) \\ x<3 \end{gathered}`[tex]0In conclusion, the answer is 0