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Linear Inequalities — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLinear Inequalities1 Mark
MCQ
The solution of the inequality $\frac{\text{x}}{4}>\frac{\text{x}}{2}+1$ will be:
  • A
    $\text{x}>4$
  • B
    $\text{x}>-4$
  • ✓
    $\text{x}<-4$
  • D
    $-4 <\text{ x} >4$
✓

Answer

Correct option: C.
$\text{x}<-4$
Given: $\frac{\text{x}}{4}>\frac{\text{x}}{2}+1$
$\Rightarrow\frac{\text{x}}{4}-\frac{\text{x}}{2}>1$
$\Rightarrow\frac{\text{x}-2\text{x}}{4}>1$
$\Rightarrow\frac{\text{-x}}{4}>1$
$\Rightarrow-\text{x}>4$
$\Rightarrow\text{x}<-4$

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