Question

Solve the inequalities for real x for the following equation: $\frac{x}{4} \ \textless \ \frac{(5x-2)}{3} -\frac{(7x-3)}{5}$

Answer 1

$\dfrac{x}{4} \ \textless \ \dfrac{(5x-2)}{3} -\dfrac{(7x-3)}{5}$

Make into single fraction:

$\dfrac{x}{4} \ \textless \ \dfrac{5(5x-2)}{15} -\dfrac{3(7x-3)}{15}$

$\dfrac{x}{4} \ \textless \ \dfrac{5(5x-2) - 3(7x - 3)}{15}$

$\dfrac{x}{4} \ \textless \ \dfrac{25x - 10-21x + 9}{15}$

$\dfrac{x}{4} \ \textless \ \dfrac{4x - 1}{15}$

Multiply 4 and 15:

$15x \ \textless \ 4(4x - 1)$

Distribute 4:

$15x \ \textless \ 16x - 4$

Subtract 16x from both sides:

$15x - 16x \ \textless \ - 4$

$-x \ \textless \ - 4$

Divide by -1:

$x \ \textgreater 4$