Question

Solve: $\frac{3x+5}{5}-\frac{x-2}{3}=\frac{5x-7}{6}$.

Answer 1

Given, $\frac{3x+5}{5}-\frac{x-2}{3}=\frac{5x-7}{6}$

$⟹$ $\frac{3(3x+5)-5(x-2)}{5\times 3}=\frac{5x-7}{6}$ …[Cross-multiplying the denominators on the LHS]

$⟹$ $\frac{9x+15-5x+10}{5\times 3}=\frac{5x-7}{6}$ ...[By Distribution Law]

$⟹$ $\frac{4x+25}{5}=\frac{5x-7}{2}$ ...[Multiplying $3$ on both sides and simplifying]

$⟹$ $(4x+25)2=(5x-7)5$ …[Cross-multiplying the denominators]

$⟹$ $8x+50=25x-35$ ...[By Distribution Law]

$⟹$ $35+50=25x-8x$ ...[Transposing $x$ terms to one side]

$⟹$ $17x=85$ ...[On simplifying]

$⟹$ $x=\frac{85}{17}$ ...[Dividing $175$ on both sides]

$⟹$ $x=5$.