Question

How do you solve `7x/8-3x/5=11/2`?

Answer 1

`x=20`

Explanation:

Solve:

`7 x/8-3 x/5=11/2`

Simplify `7xx x/8` to `(7x)/8`.

`(7x)/8-3 x/5=11/2`

Simplify `3 x/5` to `(3x)/5`.

`(7x)/8-(3x)/5=11/2`

In order to add or subtract fractions, they must have the same denominator, which is the least common denominator (LCD). To find the LCD, list the multiples of each denominator and find the lowest multiple they have in common.

`8:` `8,16,24,32,color(red)40,48,...`
`5:` `5,10,15,20,25,30,35,color(red)40,...`

The LCD is `40`.

Multiply each fraction by an equivalent fraction that will give both fractions the same denominator. An `color(red)"equivalent fraction"` is equal to `1`, such as `2/2=1`, so it doesn't change the amount.

`(7x)/8xxcolor(red)(5/5)-(3x)/5xxcolor(red)(8/8)=11/2`

Simplify.

`(35x)/40-(24x)/40=11/2`

`(11x)/40=11/2`

Multiply both sides by `40`

`11x=440/2`

Simplify `440/2` to `220`.

`11x=220`

Divide both sides by `11`.

`x=220/11`

`x=20`

Answer 2

`x = -20`

Explanation:

I will treat the fractions as mixed numbers of the form `a b/c`

Convert the mixed numbers to improper fractions.

`a b/c= (axxc +b)/c`

`7 x/8 -3 x/5 = 11/2`

`(56+x)/8 -(15+x)/5 = 11/2`

To subtract fractions, find a common denominator.

`(5(56+x))/40 -(8(15+x))/40 = (11xx20)/(2xx20)`

`(280+5x-120-8x)/40 =220/40`

`:. 280+5x-120-8x=220" "larr`solve for `x`

`280-120-220 = 8x-5x`

`-60 =3x`

`x=-20`

Answer 3

`color(magenta)(x=20`

Explanation:

`7 x/8-3 x/5=11/2`

`:.(7 xx x/8)-(3 xx x/8)=11/2`

`:.(7x)/8-(3x)/5=11/2`

`:.(35x-24x=220)/40`

multiply both sides by 40

`:.35x-24x=220`

`:.11x=220`

`:.color(magenta)(x=20`

~~~~~~~~~~~~~~~~~

`color(magenta)(check:-`

`:.7(color(magenta)20/8)-3(color(magenta)20/5)=11/2`

`:.140/8-60/5=11/2`

`:.17.5-12=11/2`

`:.5.5=11/2`

`:.color(magenta)(5.5=5.5`