Question

solve 5x +(x-1-x/2)-(7x-1)+1/2=0 hence find m if 1/x+m=3​

Answer 1

Given-

$\bf \: 5x + (x - 1 - \frac{x}{2} ) - 7x + 1 + \frac{1}{2} = 0$

and

$\bf \frac{1}{x + m } = 3 \\ \implies \bf 3x + 3m = 1 \\ \implies \boxed{ \bf \: m = - x}$

First we find the value of x

$\bf \: 5x + x - 1 - \frac{x}{2} - 7x + 1 + \frac{1}{2} = 0 \\ \implies \bf \: 10x + 2x - 2 - x - 14x + 2 + 1 = 0 \\ \implies \bf - 3x + 1 = 0 \\ \implies \boxed{ \bf \: x = \frac{1}{3} }$

Therefore

$\boxed { \huge \: m = - \frac{1}{3}}$