Question

The interval(s) which satisfies the solution set of the inequality $4x-2>x-\frac{3-x}{4}>3$ is/are

• A. $x>\frac{5}{11}$
• B. $\frac{5}{11}<x<3$
• C. $x>3$
• D. $x<3$

Answer 1

The correct option is C $x>3$

$4x-2>x-\frac{3-x}{4}>3$
Split the inequality in two parts
$4x-2>x-\frac{3-x}{4}$ and $x-\frac{3-x}{4}>3$
Now,
$4x-2>\frac{4x-(3-x)}{4}$
$\Rightarrow 16x-8>5x-3$
$\Rightarrow 11x>5$
$\Rightarrow x>\frac{5}{11}...\left(1\right)$
and
$x-\frac{3-x}{4}>3$
$\Rightarrow 5x-3>12$
$\Rightarrow x>3...\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\Rightarrow x>3$