Question

`(x)/(9) - (x + 2)/(3) = 12`
​

Answer 1

`x = -57`

Explanation:

-Solve for the value of x :

`(x)/(9) - (x+2)/(3) = 12`

-Multiply both sides by
`9` and the least common multiple of
`9` is
`3` :

`9* (x)/(9) - (x+2)/(3) = 12 * 9`

`x - 3 (x + 2) = 108`

-Use Distributive Property :

`x - 3 (x + 2) = 108`

`x - 3x - 6 = 108`

-Combine both
`x` and
`-3x` :

`x - 3x - 6 = 108`

`-2x - 6 = 108`

-Add both sides by
`6` :

`-2x - 6 + 6 = 108 + 6`

`-2x = 114`

-Divide both sides by
`-2x` :

`(-2x)/(-2) = (114)/(-2)`

`x = -57`

So, the value of x is
`-57`.

Answer 2

`\boxed{ \bold{ \huge{ \boxed{ \sf{x = 57}}}}}`

Explanation:

`\sf{ (x)/(9) - (x + 2)/(3) = 12}`

Take the L.C.M of 9 and 3

To do so, First of all find the prime factors of each numbers.

9 = 3 × 3 × 1

3 = 3 × 1

Take out the common prime factors i.e 3 and 1

Also take out the other remaining prime factor : 3

Multiply those all prime factors and obtain L.C.M

= 3 × 3 × 1 = 9

L.C.M of 9 and 3 = 9

`\longrightarrow{ \sf{ (x - 3(x + 2))/(9) = 12}}`

Distribute 3 through the parentheses

`\longrightarrow{ \sf{ (x - 3x - 6)/(9) = 12}}`

Collect like terms

`\longrightarrow{ \sf{ ( - 2x - 6)/(9) = 12}}`

Do cross multiplication

`\longrightarrow{ \sf{ - 2x - 6 = 12 * 9}}`

Multiply the numbers: 12 and 9

`\longrightarrow{ \sf{ - 2x - 6 = 108}}`

Move 6 to right hand side and change it's sign

`\longrightarrow{ \sf{ - 2x = 108 + 6}}`

Add the numbers: 108 and 6

`\longrightarrow{ \sf{ - 2x = 114}}`

Divide both sides by -2

`\longrightarrow{ \sf{ ( - 2x)/( - 2) = (114)/( - 2) }}`

Calculate

`\longrightarrow{ \sf{x = - 57}}`

Hope I helped!

Best regards! :D