# How do you solve \frac { 6x - 1} { 5} - \frac { 5x - 1} { 6} = 4x - 1?

Jul 5, 2017

$x = + \frac{29}{109}$

#### Explanation:

Given:$\text{ } \frac{6 x - 1}{5} - \frac{5 x - 1}{6} = \frac{4 x - 1}{1}$

The denominator of 1 is both correct and very deliberate.
Not normally written this way though!

color(green)([(6x-1)/5color(red)(xx1)]-[(5x-1)/6color(red)(xx1)]=(4x-1)/1color(red)(xx1)

color(green)([(6x-1)/5color(red)(xx6/6)]-[(5x-1)/6color(red)(xx5/5)]=(4x-1)/1color(red)(xx30/30)

$\frac{36 x - 6}{30} - \frac{25 x - 5}{30} \text{ "=" } \frac{120 x - 30}{30}$

Multiply both sides by 30.

Another way of looking at it is: as they all have the same denominator then as the whole is true then just equating the numerators to each other is equally true.

$36 x - 6 - 25 x + 5 = 120 x - 30$

$11 x - 1 \text{ "=" } 120 x - 30$

$109 x = + 29$

$x = + \frac{29}{109}$