If | x + 5 | 10 , then

Question

If $| x + 5 |$ $\geq 10$ , then

Smart Achievers · Accepted Answer

(3)

We know that $| x - a |$ $\geq r$

$\Leftrightarrow$ $x \leq a - r or x \geq a + r$

$∴$ $| x + 5 |$ $\geq 10 \Leftrightarrow x \leq - 5 - 10, or x \geq - 5 + 10$

$\Leftrightarrow$ $x \leq - 15 or x \geq 5 \Leftrightarrow x \in (- \infty, - 15] or x \in [5, \infty)$

$\Leftrightarrow$ $x \in (- \infty, - 15] \cup [5, \infty)$

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