Linear Equation Problem

Question

Evaluating the expression below:

$\displaystyle \frac{2(6-x)}{3} = \frac{9(x+5)}{6} + \frac{1}{3}$

The answer is $-\frac{23}{13}$ but to obtain this answer what specific method do you use?

Answer 1

Given the equation:

$\dfrac{2(6-x)}{3} = \dfrac{9(x+5)}{6} + \dfrac 13$

First of all you want to get rid of the divisors. For that, multiply per 6, so you get:

$4(6-x) = 9(x+5) + 2$

Then expand the parenthesis:

$24 - 4x = 9x + 45 + 2$

And move x's to one side by adding $+4x$ in both sides:

$24 - 45 -2 - 4x +4x = 9x + 4x$

$24 - 45 -2 = 9x + 4x$

Which becomes:

$24 - 47 = 13x$

$-23 = 13x$

Isolating $x$ it yields:

$x = -23/13$