Question

Solve the system of inequalities: $-4x+1\ge 0,3-4x<0$

• A. $\frac{1}{4}\ge x$
• B. $-\frac{1}{4}\ge x$
• C. $\frac{5}{4}\le x\le 3$
• D. No solution

Answer 1

The correct option is D No solution

Consider the first inequality
$-4x+1\ge 0$
$\Rightarrow 1\ge 4x$
$\Rightarrow \frac{1}{4}\ge x$...(i)
Consider the second inequality
$3-4x<0$
$\Rightarrow 3<4x$
$\Rightarrow \frac{3}{4}<x$ ...(ii)
Hence, no common region on the number line.