Question

How do you solve `(5x)/2 - x = x/14 + 9/7`?

Answer 1

`x = 9/10`

Explanation:

`(5x)/2 - x = x/14 + 9/7`

Let's get a common denominator for the left side of the equation

`(5x)/2 - x xx 2/2 = x/14 + 9/7`

`(5x - 2x)/2 = x/14 + 9/7`

`(3x)/2 = x/14 + 9/7`

Let's get all the `x`s on the same side

`(3x)/2 - x/14 = 9/7`

Common denominator

`7/7 xx (3x)/2 - x/14 = 9/7`

`(21x)/14 - x/14 = 9/7`

Let's get another common denominator (we don't technically need this, but it makes the math easier later)

`(20x)/14 = 9/7 xx 2/2`

`(20x)/14 = 18/14`

Multiply both sides by `14`

`20x = 18`

Divide by `20` on both sides

`x = 18/20`

`x = 9/10`

Answer 2

`x=9/10`

Explanation:

We have an equation which has fractions.

`(5x)/2 - x = x/14 + 9/7`

We can get rid of the fractions immediately by multiplying the whole equation by the LCM of the denominators, which is `14`

`(color(blue)(cancel14^7xx)5x)/cancel2 -color(blue)(14xx) x = (color(blue)(cancel14xx)x)/cancel14 + (color(blue)(cancel14^2xx)9)/cancel7" "larr` cancel

`" "35x -14x = x+18`

`35x-14x-x= 18`

`color(white)(xxxxxxxx)20x = 18`

`color(white)(xxxxxxxxx)x= 18/20`

`color(white)(xxxxxxxxx)x=9/10`