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Question

Mathematics Question on linear inequalities

If ∣x−3∣<2x+9|x - 3| < 2x + 9 then xx lies in the interval

A

(−∞,−2)(- \infty\quad, -2)

B

(−2,0)(-2,0)

C

(−2,∞)(-2,\infty\quad)

D

(2,∞)(2,\infty\quad)

Answer

(−2,∞)(-2,\infty\quad)

Explanation

Solution

∣x−3∣<2x+9|x-3| < 2 x+9
⇒−(2x+9)<x−3<2x+9\Rightarrow-(2 x+9) < x-3<2 x+9
⇒−2x−9<x−3\Rightarrow-2 x-9 < x-3
and x−3<2x+9x-3<2 x+9 < br/>
⇒−3x<6\Rightarrow -3 x<6 and −x<12-x < 12
⇒x>−2\Rightarrow x>-2 and x>−12x > -12
⇒x>−2\Rightarrow x > -2
∴x∈(−2,∞)\therefore x \in(-2, \infty)