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Mathematics Question on linear inequalities

If ∣x+5∣≥ 10|x + 5| \ge \,10 , then

A

x∈(−15,5]x \in ( - 15 , 5 ]

B

x∈(−5,5]x \in ( - 5 , 5 ]

C

x∈(−∞,−15]∪[5,∞)x \in ( - \infty , - 15] \cup [5, \infty)

D

x∈[−∞,−15]∪[5,∞)x \in [ - \infty , - 15] \cup [5, \infty)

Answer

x∈(−∞,−15]∪[5,∞)x \in ( - \infty , - 15] \cup [5, \infty)

Explanation

Solution

Given ∣x+5∣ ≥ 10| x + 5 | \, \ge \,10
⇒ x+5≤−10\Rightarrow \, x + 5 \le - 10 or x+5≥ 10x + 5 \ge \,10
⇒ x≤−15\Rightarrow \, x \le - 15 or x≥ 5x \ge\, 5
⇒ x∈(−∞,−15]∪[5,∞)\Rightarrow \, x \in (- \infty, -15] \cup [5, \infty)