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

1 Answer
Tony B
Jul 5, 2017

#x=+29/109#

Explanation:

Given:#" "(6x-1)/5-(5x-1)/6=(4x-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)#

#(36x-6)/30-(25x-5)/30" "=" "(120x-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.

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

#11x-1" "=" "120x-30#

#109x=+29#

#x=+29/109#

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