Question

How to solve |3x-6|<30

Answer 1

`Solution, solve\:for\:x,\:\left|3x-6\right|<30\quad :\quad -8<x<12`

`Steps:`

`|f\left(x\right)|<a\quad \Rightarrow \:f\left(x\right)<a\quad \mathrm{and}\quad \:f\left(x\right)>-a, 3x-6<30\quad \quad \mathrm{and}\quad \:\quad \:3x-6>-30`

`3x-6<30\quad :\quad x<12`

`3x-6>-30\quad :\quad x>-8`

`\mathrm{Combine\:the\:ranges}, -8<x<12`

The correct answer is -8<x<12

Answer 2

`|3x-6|<30 \\\\|x-2|<10\\\\x-2<10 \wedge x-2>-10\\\\x<12 \wedge x>-8\\\\x\in(-8,12)`