Question

Solve the following inequations $\frac{5x-2}{3}-\frac{7x-3}{5}>\frac{x}{4}$

Answer 1

$\frac{5x-2}{3}-\frac{7x-3}{5}>\frac{x}{4}\Rightarrow \frac{5(5x-2)-3(7x-3)}{15}>\frac{x}{4}\Rightarrow \frac{25x-10-21x+9}{15}>\frac{x}{4}$
$\frac{4x-1}{15}>\frac{x}{4}\Rightarrow 4(4x-1)>15x$
[Multiplying both sides by 60 i.e. Lcm of 15 and 4]
$16x-4>15x$ $\Rightarrow 16x-15x>4$[Transposing 15 x to LHS and -4 to RHS]
x > 4 $\Rightarrow x\in (4,\infty )$
Hence the solution set of the given inequation is $(4,\infty )$ This can be graphed on the real number line as shown in figure