Solve the following linear inequations in R: 7x-5 8x+3 >4 - Vidyadip

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 $\Big(\frac{-17}{25},\frac{-3}{8}\Big)$

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