Solve for x, the inequalities Exercises. |x-1| 5, |x| 2 - Vidyadip

Question

Solve for x, the inequalities Exercises.
$|\text{x}-1|\leq5,\ |\text{x}|\geq2$

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Answer

Given that $|\text{x}-1|\leq5,\ |\text{x}|\geq2$
$\Rightarrow-5\leq\text{x}-1\leq5$
$\Rightarrow4\leq\text{x}\leq6$
And $|\text{x}|\geq2$
$\Rightarrow\text{x}\leq-2$ or $\text{x}\geq2$
$\Rightarrow\text{x}\in(-\infty, -2)\cup({2, \infty})$
On combining (i) and (ii), we get,
$\text{x}\in(-4, -2)\cup({2, 6})$

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