Question

If $|2x-1|+|3x-4|=|5x-5|$, then complete set of values of $x$ is

• A. $(-\infty ,\frac{1}{2}]$
• B. $[\frac{1}{2},\frac{4}{3}]$
• C. $(-\infty ,\frac{1}{2}]\cup [\frac{4}{3},\infty )$
• D. $[\frac{4}{3},\infty )$

Answer 1

The correct option is C $(-\infty ,\frac{1}{2}]\cup [\frac{4}{3},\infty )$

$|2x-1|+|3x-4|=|5x-5|$
Here $5x+5=(2x-1)+(3x-4)$
So,
$(2x-1)(3x-4)\ge 0$
$(\because |x+y|=|x|+|y|,\text{then}xy\ge 0)$
$\Rightarrow (x-\frac{1}{2})(x-\frac{4}{3})\ge 0\therefore x\in (-\infty ,\frac{1}{2}]\cup [\frac{4}{3},\infty )$