Question

How do you solve `\frac { 3x - 6} { 2} + \frac { 2x + 4} { 3} = 7`?

Answer 1

`x=4`

Explanation:

Solve:

`(3x-6)/2+(2x+4)/3=7`

In order to add fractions, the denominators must be the same. BothThe least common denominator (LCD) for this equation is `6`.

Multiply each term by `6`.

`(6(3x-6))/2+(6(2x+4))/3=6xx7`

Simplify.

`(color(red)cancel(color(black)(6))^3(3x-6))/color(red)cancel(color(black)(2))^1+(color(red)cancel(color(black)(6))^2(2x+4))/color(red)cancel(color(black)(3))^1=6xx7`

`3(3x-6)+2(2x+4)=42`

Expand.

`9x-18+4x+8=42`

Simplify.

`9x+4x-18+8=42`

`13x-10=42`

Add `10` to both sides.

`13x=42+10`

`13x=52`

Divide both sides by `13`.

`x=52/13`

Reduce the fraction by dividing the numerator and denominator by `13`.

`x=(52-:13)/(13-:13)`

`x=4`

Answer 2

X=4

Explanation:

`(3x-6)/2 + (2x+4)/3 = 7`

`->(3/3) *(3x-6)/2 + (2/2)(2x+4)/3 = 7`

`->(9x-18)/6 + (4x+8)/6 = 7`

`->(9x+4x-10)/6 = 7`

`->(13x-10)/6 = 7`

`->(13x-10) = 42`
`->13x = 52`
`->x = 4`