Question

Solve the following inequalities,express the solution in interval notation and graph it 4.a)

Answer 1

The inequality is given to be:

`\mleft|x-6\mright|\ge2`

Recall the Absolute Rule:

`\mathrm{If}\: |u|\: \ge\: a,\: a\: >\: 0\: \mathrm{then}\: u\: \le\: -a\: \quad \mathrm{or}\quad \: u\: \ge\: a`

Applying this to the inequality, we have:

`\begin{gathered} x-6\ge2 \\ x\ge2+6 \\ x\ge8 \end{gathered}`

or

`\begin{gathered} x-6\le-2 \\ x\le-2+6 \\ x\le4 \end{gathered}`

Therefore, the solution to the inequality is:

`x\le\: 4\quad \mathrm{or}\quad \: x\ge\: 8`