Solve the following linear inequations in R: 5x-6 x+6 <1 - Vidyadip

Question

Solve the following linear inequations in R:
$\frac{5\text{x}-6}{\text{x}+6}<1$

✓

Answer

$\frac{5\text{x}-6}{\text{x}+6}<1$
$\frac{5\text{x}-6}{\text{x}+6}-1<0$
$\frac{5\text{x}-6-(\text{x}+6)}{\text{x}+6}<0$
$\frac{5\text{x}-6-\text{x}-6}{\text{x}+6}<0$
$\frac{4\text{x}-12}{\text{x}+6}<0$
Case 1: $4\text{x}-2>0$ and $\text{x}+6<0$
$\Rightarrow\text{x}>3$ and $\text{x}<-6$
Case 2: $4\text{x}-2<0$ and $\text{x}+6>0$
$\Rightarrow\text{x}<3$ and $\text{x}>-6$
Hence the solution set is (-6, 3)

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