Solve the following linear inequations in R: 2x+3 4 -3< x-4 3 -2 - Vidyadip

Question

Solve the following linear inequations in R:
$\frac{2\text{x}+3}{4}-3<\frac{\text{x}-4}{3}-2$

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Answer

$\frac{2\text{x}+3}{4}-3<\frac{\text{x}-4}{3}-2$
$\frac{2\text{x}+3-12}{4}<\frac{\text{x}-4-6}{3}$
3 (2x + 3 - 12) < 4 (x - 4 - 6)
3(2x - 9) < 4 (x - 10)
6x - 27 < 4x - 40
6x - 4x < -40 + 27
2x < -13
$\text{x}<-\frac{13}{2}$
$\therefore$ The solution set is $\Big(-\infty,-\frac{13}{2}\Big)$

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