Question

Solve: 2x-3/5+x+3/4=4x+1/7

Answer 1

$\huge{\underline{\underline{\red{\bf{Answer:}}}}}$

$\frac{2x - 3}{5} + \frac{x + 3}{4} = \frac{4x + 1}{7}$

$\frac{2x}{5} - \frac{3}{5} + \frac{x}{4} + \frac{3}{4} = \frac{4x}{7} + \frac{1}{7}$

$\frac{2x}{5} - \frac{x}{4} - \frac{4x}{7} = \frac{1}{7} + \frac{3}{5} - \frac{3}{4}$

$\frac{56x + 35x - 80x}{140} = \frac{20 + 84 - 105}{140}$

$\frac{11x}{140} = \frac{ - 1}{140}$

$x = \frac{ - 1}{140} \div \frac{11}{140}$

$x = \frac{ - 1}{140} \times \frac{140}{11}$

$x = \frac{ - 1}{11}$

Checking =

LHS -

$\frac{2x - 3}{ 5}$

$\frac{2( \frac{ - 1}{11}) - 3 }{5} + \frac{ \frac{ - 1}{11} + 3}{4}$

$\frac{ \frac{ - 2}{11} - \frac{ 3}{1} }{5} + \frac{ \frac{ - 1}{11} + 3}{4}$

$\frac{ \frac{ - 2 - 33}{11} }{5} + \frac{ \frac{ - 1}{11} + 3}{4}$

$\frac{ \frac{ - 35}{11} }{5} + \frac{ \frac{ - 1 }{11} + 3 }{4}$

$\frac{ - 35}{11} \times \frac{1}{5} + \frac{ \frac{ - 1}{11} + 3}{4}$

$\frac{ - 7}{11} + \frac{ \frac{ - 1}{11} + 3}{4}$

$\frac{ - 7}{11} + \frac{ \frac{ - 1 + 33}{11} }{4}$

$\frac{ - 7}{11} + \frac{32}{11} \div 4$

$\frac{ - 7}{11} + \frac{32}{11} \times \frac{1}{4}$

$\frac{ - 7}{11} + \frac{8}{11}$

$= \frac{1}{11}$

RHS -

$\frac{4x + 1}{7}$

$\frac{4( \frac{ - 1}{11}) + 1 }{7}$

$\frac{ \frac{ - 4}{11} + 1}{7}$

$\frac{ \frac{ - 4 + 11}{11} }{7}$

$\frac{7}{11} \div 7$

$\frac{7}{11} \times \frac{1}{7}$

$\frac{1}{11}$

LHS = RHS

HENCE, VERIFIED