The solution of 6 x 4 x - 1 1 2 is

Question

The solution of $\frac{6 x}{4 x - 1} < \frac{1}{2}$ is

Smart Achievers · Accepted Answer

(2)

Given inequality is, $\frac{6 x}{4 x - 1} < \frac{1}{2}$ $\Rightarrow \frac{12 x}{4 x - 1} < 1$

$\Rightarrow$ $\frac{12 x}{4 x - 1} - 1 < 0 \Rightarrow \frac{8 x + 1}{4 x - 1} < 0$ $\dots (i)$

For above inequality (i), we have two cases either

$(I)$ $8 x + 1 > 0, 4 x - 1 < 0$ or $(II)$ $8 x + 1 < 0, 4 x - 1 > 0$

From (I), we get $x > - \frac{1}{8}, x < \frac{1}{4}$

$∴$ $x \in (- \frac{1}{8}, \frac{1}{4})$ $\dots (i i)$

From (II), $x < - \frac{1}{8}, x > \frac{1}{4},$ both of which can not be true

$∴$ (ii) represents the solution set of given inequality.

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