Question

How do you solve `3= \frac { 5x - 4} { 3} + \frac { 3x - 1} { 5}`?

Answer 1

`x=2`

Explanation:

`3=(5x-4)/3+(3x-1)/5`

Multiply all terms by the LCM of `3` and `5` which is `15`.

`3xx15=15xx(5x-4)/3+15xx(3x-1)/5`

`45=5cancel15xx(5x-4)/(1cancel3)+3cancel15xx(3x-1)/(1cancel5)`

`45=5(5x-4)+3(3x-1)`

Open the brackets and simplify.

`45=25x-20+9x-3`

`45=25x+9x-20-3`

`45=(25x+9x)-(20+3)`

`45=34x-23`

Add `23` to both sides.

`45+23=34x-23+23`

`68=34x`

Divide both sides by `34`.

`68/34=(34x)/34`

`(2cancel68)/(1cancel34)=(cancel34x)/cancel34`

`2=x` or `x=2`

Answer 2

Please see the step process below;

Explanation:

`3= \frac { 5x - 4} { 3} + \frac { 3x - 1} { 5}`

First Step: Multiply via the LCM, in this case the LCM `= 15`

`15 (3/1) = 15 ((5x - 4)/3) + 15 ((3x - 1)/5)`

Second Step: Simplify

`15 (3/1) = cancel15^5 ((5x - 4)/cancel3) + cancel15^3 ((3x - 1)/cancel5)`

`15(3) = 5 (5x - 4) + 3 (3x - 1)`

`45 = 25x - 20 + 9x - 3`

Third Step: Collecting like terms

`45 = 25x + 9x - 20 - 3`

`45 = 34x - 23`

`45 + 23 = 34x`

`68 = 34x`

Divide both sides by `34`

`68/34 = (34x)/34`

`68/34 = (cancel34x)/cancel34`

`68/34 = x`

`x = 2`