Question

How do you solve `\frac { 2x } { 5} - \frac { x + 18} { 6} = 23+ \frac { x } { 30}`?

Answer 1

`x = 130`

Explanation:

Rearrange the equation. all `x`'s on one side.

`(2x)/5 - (x + 18 )/6 -x/30 = 23`

Equalize the denominators to `30`

`(2x)/5 * 6/6 - (x + 18 )/6 * 5/5 -x/30 = 23`

`(12x) / 30 - (5(x + 18)) / 30 - x/30 = 23`

`( 12x -5x -90 -x ) / 30 =23`

Multiply both sides by `30`

`12x - 5x -90 -x = 690`

`6x = 690 + 90`

`6x = 780`

`x = 780 / 6`

`x =130`

Answer 2

`x = 130`

Explanation:

`(2x)/5 - (x+18)/6 = 23 + x/30`

When you have an equation which has fractions in it, you can get rid of the fractions immediately.

Multiply each term by the LCM of the denominators and cancel.

In this case the LCM = `color(blue)(30`

`(color(blue)(30 xx)2x)/5 - (color(blue)(30 xx)(x+18))/6 = color(blue)(30 xx)23 + (color(blue)(30 xx)x)/30`

Now cancel all the denominators:

`(color(blue)(cancel30^6 xx)2x)/cancel5 - (color(blue)(cancel30^5 xx)(x+18))/cancel6 = color(blue)(30 xx)23 + (color(blue)(cancel30 xx)x)/cancel30`

`6 xx2x-5(x+18)= 30xx23 +x" "larr` no fractions!! Simplify

`12x-5x-90 = 690+x" "larr` now solve the equation

`12x-5x-x = 690+90" "larr` re-arrange the terms

`6x = 780" "larr div 6` on both sides

`x = 130`