Question

The set of solutions for $\frac{4x}{3}-\frac{9}{4}<x+\frac{3}{4}$ and $\frac{7x-1}{3}-\frac{7x+2}{6}>x$ is

• A. $(4,9)$
• B. $(2,9)$
• C. $(6,9)$
• D. $(4,6)$

Answer 1

The correct option is A $(4,9)$

$\frac{4x}{3}-\frac{9}{4}<x+\frac{3}{4}\Rightarrow \frac{x}{3}<3\Rightarrow x<9\cdots \left(1\right)$

$\frac{7x-1}{3}-\frac{7x+2}{6}>x\Rightarrow 14x-2-7x-2>6x\Rightarrow x>4\cdots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,
$x\in (4,9)$