Linear Inequations — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequations3 Marks
Question
Solve the following linear inequations in R: $\frac{\text{x}-1}{\text{x}+3}>2$
✓
Answer
$\frac{\text{x}-1}{\text{x}+3}>2$ $\frac{\text{x}-1}{\text{x}+3}-2<0$ $\frac{\text{x}-1-2(\text {x}+3)}{\text{x}+3}>0$ $\frac{\text{x}-1-2\text{x}-6}{\text{x}+3}>0$ $\frac{-\text{x}-7}{\text{x}+3}>0$ $\frac{\text{x}+7}{\text{x}+3}<0$ Case 1: $\text{x}+7>0$ and $\text{x}+3<0$ $\Rightarrow\text{x}>-7$ and $\text{x}>-3$ Case 2: $\text{x}+7<0$ and $\text{x}+3>0$ $\Rightarrow\text{x}<-7$ and $\text{x}>-3$ This is not possible. $\therefore$ The solution set is (-7, -3)
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