Question

solve the linear equation and check the result​

Answer 1

GIVEN :-

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

TO FIND :-

• Value of 'x'.

HOW TO SOLVE MIX FRACTION ?

$\\ \sf \:p \dfrac{q}{r} = \dfrac{(p \times r) + q}{r}$

SOLUTION :-

We have ,

$\\ \implies \sf \: \dfrac{x}{3} - \dfrac{x}{5} + \dfrac{2x}{7} - \dfrac{3x}{4} = 3 \dfrac{1}{2} \\ \\ \\ \implies\sf \: \left( \dfrac{x}{3} - \dfrac{x}{5} \right) + \left( \dfrac{2x}{7} - \dfrac{3x}{4} \right) = \dfrac{(3 \times 2) + 1}{2}$

Taking L.C.M and solving , we get..

$\\ \implies \sf \: \left( \dfrac{5x - 3x}{15} \right) + \left( \dfrac{8x - 21x}{28} \right) = \dfrac{7}{2}$

Solving furthur ..

$\\ \implies\sf \: \dfrac{2x}{15} - \dfrac{13x}{28} = \dfrac{7}{2}$

Again by taking L.C.M and solving we get..

$\\ \implies\sf \: \dfrac{28(2x) - 15(13x)}{15 \times 28} = \dfrac{7}{2} \\ \\ \\ \implies \sf \: \dfrac{56x - 195x}{420} = \dfrac{7}{2} \\ \\ \\ \implies \sf \: \dfrac{139x}{420} = \dfrac{7}{2} \\ \\ \\ \implies \sf \: x = \dfrac{7}{2} \times \dfrac{420}{139} \\ \\ \\ \implies\sf \: x = \dfrac{2940}{278} \\ \\ \\ \implies\boxed{ \sf \: x = { \dfrac{735}{69} }}$