If $8+3x < |8+3x|, x\in R,$ then x li

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

If $8+3x < |8+3x|, x\in R,$ then x lies in :

Options:

(-∞, ∞)

$\left(-∞, \frac{-3}{8}\right)$

$\left(-∞, \frac{-8}{3}\right)$

$\left(-∞, \frac{8}{3}\right)$

Correct Answer:

$\left(-∞, \frac{-8}{3}\right)$

Explanation:

The correct answer is Option (3) → $\left(-∞, \frac{-8}{3}\right)$

CASE 1: $8+3x>0$

$⇒8+3x<8+3x$

$⇒0<0$

This is never true, no solution.

CASE 2: $8+3x<0$

$⇒8+3x<-(8+3x)$

$⇒8+3x+3x<-8$

$⇒6x<-16$

$⇒x<\frac{-8}{3}$