Solve the following linear inequations in R: 5x+8 4-x <2 - Vidyadip

Question

Solve the following linear inequations in R:
$\frac{5\text{x}+8}{4-\text{x}}<2$

✓

Answer

$\frac{5\text{x}+8}{4-\text{x}}<2$
$\frac{5\text{x}+8}{4-\text{x}}-2<0$
$\frac{5\text{x}+8-2(4-\text {x})}{4-\text{x}}<0$
$\frac{5\text{x}+8-8+2\text{x}}{4-\text{x}}<0$
$\frac{7\text{x}}{4-\text{x}}<0$
Case 1: $7\text{x}>0$ and $4-\text{x}<0$
$\Rightarrow\text{x}>0$ and $4<\text{x}$
$\Rightarrow\text{x}<0$
Hence solution set is $(-\infty,0)\cup(4,\infty)$

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