Solve the following linear inequations in R: 3 x-2 <1 - Vidyadip

Question

Solve the following linear inequations in R:
$\frac{3}{\text{x}-2}<1$

✓

Answer

$\frac{3}{\text{x}-2}<1$
$\frac{3}{\text{x}-2}-1<0$
$\frac{3-(\text{x}-2)}{\text{x}-2}<0$
$\frac{3-\text{x}+2}{\text{x}-2}<0$
$\frac{5-\text{x}}{\text{x}-2}<0$
$\frac{\text{x}-5}{\text{x}-2}>0$
Case1: x - 5 > 0 and x - 2 > 0
⇒ x > 5 and x > 2
⇒ x > 5
Case 2: x - 5 < 0 and x - 2 < 0
⇒ x < 5 and x < 2
⇒ x < 2
$\therefore$ solution set is $(-\infty,2)\cup(5,\infty)$

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