Linear Inequations — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequations3 Marks
Question
Solve the following linear inequations in R: $\frac{7\text{x}-5}{8\text{x}+3}>4$
✓
Answer
$\frac{7\text{x}-5}{8\text{x}+3}>4$ $\frac{7\text{x}-5}{8\text{x}+3}-4>0$ $\frac{7\text{x}-5-4(8\text{x}+3)}{8\text{x}+3}>0$ $\frac{7\text{x}-5-32\text{x}-12}{8\text{x}+3}>0$ $\frac{-25\text{x}-17}{8\text{x}+3}>0$ $\frac{25\text{x}+17}{8\text{x}+3}<0$ Case 1: $25\text{x}+17>0$ and $8\text{x}+3<0$ $\Rightarrow\text{x}>\frac{-17}{25}$ and $\text{x}<\frac{-3}{8}$ Case 2: $25\text{x}+17<0$ and $8\text{x}+3>0$ $\Rightarrow\text{x}<\frac{-17}{25}$ and $\text{x}>\frac{-3}{8}$ This is not possible $\therefore$ Hence the solution set is $\Big(\frac{-17}{25},\frac{-3}{8}\Big)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.