Linear Inequations — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequations3 Marks
Question
Solve the following linear inequations in R: $\frac{\text{x}}{\text{x}-5}>\frac{1}{2}$
✓
Answer
$\frac{\text{x}}{\text{x}-5}>\frac{1}{2}$ $\frac{\text{x}}{\text{x}-5}-\frac{1}{2}>0$ $\frac{2\text{x}-(\text{x}-5)}{2(\text{x}-5)}>0$ $\frac{2\text{x}-\text{x}+5}{2\text{x}-10}>0$ $\frac{\text{x}+5}{2\text{x}-10}>0$ Case 1: $\text{x}+5>0$ and $2\text{x}-10>0$ $\Rightarrow\text{x}>-5$ and $\text{x}>5$ $\Rightarrow\text{x}>5$ Case 2: $\text{x}+5<0$ and $2\text{x}-10<0$ $\Rightarrow\text{x}<-5$ and $\text{x}<5$ $\Rightarrow\text{x}<-5$ Hence the solution set is $(-\infty,-5)\cup(5,\infty)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.