Question

Solve each of the following equations and also check your results in each case:

(v) $\frac{1}{2}x+7x-6=7x+\frac{1}{4}$

Answer 1

Given: $\frac{1}{2}x+7x-6=7x+\frac{1}{4}$

$\Rightarrow \frac{1}{2}x+7x-7x=\frac{1}{4}+6$

$\Rightarrow \frac{1}{2}x=\frac{1+24}{4}$

$\Rightarrow \frac{1}{2}x=\frac{25}{4}$

$\Rightarrow 4x=25\times 2$

$\Rightarrow x=\frac{50}{4}$

$\Rightarrow x=\frac{25}{2}$

To check: $\frac{1}{2}x+7x-6=7x+\frac{1}{4}\text{for}x=\frac{25}{2}$

$L.H.S=\frac{1}{2}x+7x-6$

$=\left(\frac{1}{2}\right)\left(\frac{25}{2}\right)+7\left(\frac{25}{2}\right)-6$

$=\frac{25}{4}+\frac{175}{2}-6$

$=\frac{25+350-24}{4}$

$=\frac{351}{4}$

$R.H.S=7x+\frac{1}{4}$

$=7\left(\frac{25}{2}\right)+\frac{1}{4}$

$=\frac{175}{2}+\frac{1}{4}$

$=\frac{350+1}{4}$

$=\frac{351}{4}$

Hence, the given equation is verified for $x=\frac{25}{2}$.