If |x + 5| <= |2x - 5|, which of the following specifies all the value of x ? : Crackverbal Support

If |x + 5| <= |2x - 5|, which of the following specifies all the value of x ? Print

Modified on: Tue, 12 Oct, 2021 at 1:33 PM

Concept: The question tests on the application skills in inequality

Solution:

|x+5|≤|2x−5|

on squaring both sides:

x^2 + 10x + 25 ≤ 4x^2 − 20x + 25

=>-3x^2 + 30x <=0

=> -x^2 +10x < = 0

Multiply with -1 and flip the sign

=>x^2−10 x ≥ 0
=> x(x−10)≥0 hence the critical points are 0 and 10.

Both are of same sign.

Using the wavy curve approach, x<=smallest critical point or x>=greatest critical point in this case.

Refer to wavy curve approach explained in the session o Inequality

=>x≤0 or x≥ 10

(option d)

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If |x + 5| &lt;= |2x - 5|, which of the following specifies all the value of x ? Print