Question

Find the solution set of this inequality. Enter your answer in interval notation using grouping symbols

Answer 1

Given

The inequality,

`|6x-12|\leq6`

To find the solution set.

Step-by-step explanation:

It is given that,

The inequality is,

`|6x-12|\leq6`

That implies,

`\begin{gathered} |6x-12|\leq6 \\ \Rightarrow-6\leq6x-12\leq6 \\ \Rightarrow-6+12\leq6x-12+12\leq6+12 \\ \Rightarrow6\leq6x\leq18 \\ (/ by\text{ }6)\Rightarrow1\leq x\leq3 \end{gathered}`

Hence, the solution set is given by

`x\in[1,3]`