Question

How do you solve `\frac { 2x + 12} { 3x - 6} = \frac { 10} { 11}`?

Answer 1

See a solution process below:

Explanation:

First do a cross product or cross multiply the equation:

`11(2x + 12) = 10(3x - 6)`

Next, expand the terms in parenthesis on each side of the equation by multiplying each of the terms within the parenthesis by the term outside the parenthesis:

`color(red)(11)(2x + 12) = color(blue)(10)(3x - 6)`

`(color(red)(11) xx 2x) + (color(red)(11) xx 12) = (color(blue)(10) xx 3x) - (color(blue)(10) xx 6)`

`22x + 132 = 30x - 60`

Then, subtract `color(red)(22x)` and add `color(blue)(60)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(22x) + 22x + 132 + color(blue)(60) = -color(red)(22x) + 30x - 60 + color(blue)(60)`

`0 + 192 = (-color(red)(22) + 30)x - 0`

`192 = 8x`

Now, divide each side of the equation by `color(red)(8)` to solve for `x` while keeping the equation balanced:

`192/color(red)(8) = (8x)/color(red)(8)`

`24 = x`

`x = 24`