Question

4,
(e) Find value (6 - 2x)(2 + x) for x =
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Answer 1

Answer:

hlo good morning dear

kaisa ho ap

Answer 2

Step-by-step explanation:

(|x – 6| > |3x + 6| \implies |x – 6| - |3x + 6|>0\)

If \(x<-2\) we have \((6-x)-(-3x-6)=6-x+3x+6=2x+12 > 0 \implies x >-6\). Hence \(-6 <x <-2\)

If \(-2 \leq x < 6\) we have \((6-x)-(3x+6)=-4x>0 \implies x<0\). Hence \(-2 \leq x < 0\)

If \(x \geq 6\) we have \((x-6)-(3x+6)=-2x-12>0 \implies x<-6\). There is no satisfied value of \(x\) in this case.

Combine all cases we have \(-6 < x < 0\).

Thus, \(x\) could receive 5 integer value \(\{-5;-4;-3;-2;-1\}\)

The answer is C.

Solution 2.

\(|x – 6| > |3x + 6| \implies (x-6)^2 > (3x+6)^2\)

\(\implies x^2-12x+36 > 9x^2+36x+36 \implies 8x^2+48x<0\)

\(\implies 8x(x+6)<0 \implies -6<x<0\).