2 x+3 3 3 x-1 4 where x is positive even integer. - Vidyadip

Question

$\frac{2 x+3}{3} \geq \frac{3 x-1}{4}$ where $x$ is positive even integer.

✓

Answer

$
\begin{aligned}
& \frac{2 x+3}{3} \geq \frac{3 x-1}{4} \\
& \Rightarrow \frac{2 x}{3}+\frac{3}{3} \geq \frac{3 x}{4}-\frac{1}{4} \\
& \Rightarrow \frac{2 x}{3}-\frac{3 x}{4} \geq \frac{-1}{4}-1 \\
& \Rightarrow \frac{8 x-9 x}{12} \geq-\frac{5}{4} \\
& \Rightarrow \frac{-x}{12} \geq \frac{-5}{4} \\
& \Rightarrow \frac{x}{12} \leq \frac{5}{4} \\
& \Rightarrow x \leq \frac{5}{4} \times 12 \\
& \Rightarrow x \leq 15
\end{aligned}
$
$\because x$ is positive even integer
$
\therefore x=\{2,4,6,8,10,12,14\} .
$

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