Question

Solve each of the following equations and also check your results in each case:​
$\frac{3}{4}x+4x=\frac{7}{8}+6x-6$

Answer 1

Given: $\frac{3}{4}x+4x=\frac{7}{8}+6x-6$

$\Rightarrow \frac{3}{4}x+4x-6x=\frac{7}{8}-6$

$\Rightarrow \frac{3x+16x-24x}{4}=\frac{7-48}{8}$

$\Rightarrow -\frac{5x}{4}=-\frac{41}{8}$

$\Rightarrow -5x\left(8\right)=-41\left(4\right)$

$\Rightarrow -40x=-164$

$\Rightarrow x=\frac{-164}{-40}=\frac{82}{20}$

$\Rightarrow x=\frac{41}{10}$

To check :$\frac{3}{4}x+4x=\frac{7}{8}+6x-6\text{for}x=\frac{41}{10}$

$L.H.S=\frac{3}{4}x+4x$

$=\left(\frac{3}{4}\right)\left(\frac{41}{10}\right)+4\left(\frac{41}{10}\right)$

$=\frac{123}{40}+\frac{164}{10}$

$=\frac{123+656}{40}$

$=\frac{779}{40}$

$R.H.S=\frac{7}{8}+6x-6$

$=\frac{7}{8}+6\left(\frac{41}{10}\right)-6$

$=\frac{7}{8}+\frac{246}{10}-6$

$=\frac{70+1968-480}{80}$

$=\frac{1558}{80}$

$=\frac{779}{40}$

$\therefore L.H.S=R.H.S$

Hence, the given equation is verified for $x=\frac{41}{10}$.