Question

The range of values of $x$ for which the inequality $\frac{3x-2}{5x-3}\ge 4$ is satisfied is given by

• A. $(\frac{2}{3},\frac{3}{5})$
• B. $[\frac{-8}{3},\frac{12}{5})$
• C. $[\frac{10}{17},\frac{3}{5})$
• D. $[\frac{-3}{5},\frac{12}{5}]$

Answer 1

The correct option is C

$[\frac{10}{17},\frac{3}{5})$

$\frac{3x-2}{5x-3}\ge 4$

We can't cross multiply 4 with (5x - 3) as (5x - 3) can be negative or positive.

$\frac{3x-2}{5x-3}-4\ge 0$

$\frac{3x-2-(20x-12)}{5x-3}\ge 0$

$\frac{-17x+10}{5x-3}\ge 0$

$\Rightarrow$ $\frac{17x-10}{5x-3}\le 0$ This inequality is not defined for $x=\frac{3}{5}$

Sign scheme of $\frac{17x-10}{5x-3}$ is shown below

From above diagram, $x\in [\frac{10}{17},\frac{3}{5})$