MCQ
If $|\text{x}+3|\geq10,$ then:
- A$\text{x}\in(-12,7]$
- B$\text{x}\in(-13,7)$
- C$\text{x}\in(\infty,-13)\cup(7,\infty)$
- D$\text{x}\in(-\infty,-13]\cup[7,\infty)$
✓
Answer
- $\text{x}\in(-\infty,-13]\cup[7,\infty)$
Solution:
$|\text{x}+3|\geq10$
$\Rightarrow\text{x}+3\geq10\text{ or }\text{x}+3;\leq-10$
$\Rightarrow\text{x}\geq10-3\text{ or }\text{x}\leq-10-3$
$\Rightarrow\text{x}\geq7\ \text{or}\ \text{x}\leq-13$
$\Rightarrow\text{x}\in(-\infty,-13)\cup[7,\infty)$
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