Question

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

• A. $x>\frac{3}{8}$
• B. $x>\frac{4}{7}$
• C. $x>\frac{11}{16}$
• D. No solution

Answer 1

The correct option is D No solution

$-4x+1\ge 0$

Add $-1$ both sides we get

$-4x+1-1\ge 0+(-1)$

$\Rightarrow -4x\ge -1$

Divided both sides by -4 we get

$x\le \frac{1}{4}$ ...... $\left(i\right)$

Also,

$3-4x<0$

Add $-3$ both sides we get

$3-4x-3<0-3$

$\Rightarrow -4x<-3$

Divided by $-4$ both sides we get

$x>\frac{3}{4}$ ...... $\left(ii\right)$

Then, $\frac{3}{4}<x\le \frac{1}{4}$ which is not possible

Thus, there is no solution.