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

Solve the following inequalities,express the solution in interval notation and graph-example-1
User Kofi
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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

User Nilufer
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