Question

How do you evaluate `\frac { 3x - 4} { 5} - \frac { x + 1} { 4} = \frac { 2x - 4} { 3}`?

Answer 1

`x=\frac{17}{19}`

Explanation:

`\frac{3x-4}{5}-\frac{x+1}{4}=\frac{2x-4}{3}`

Let's multiply every fraction by `60` that is the Least Common Multiplier:
`\frac{3x-4}{5}*60-\frac{x+1}{4}*60=\frac{2x-4}{3}*60`

Now remove the denominator with the semplification:
`(3x-4)*12-(x+1)*15=(2x-4)*20`

`36x-48-15x-15=40x-80`

Move all the terms with the `x` to the left, and all the constants to the right by changing sign in both cases:
`36x-15x-40x=48+15-80`

`-19x = -17`

Multiply by `-1`, so in this way we obtain a positive x:
`-19x * (-1) = -17 * (-1)`
`19x=17`

Final result
`x=\frac{17}{19}`