Question

How do you solve `4( 2x + 3) = 3( 3x + 2)`?

Answer 1

See a solution process below:

Explanation:

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

`color(red)(4)(2x + 3) = color(blue)(3)(3x + 2)`

`(color(red)(4) xx 2x) + (color(red)(4) xx 3) = (color(blue)(3) xx 3x) + (color(blue)(3) xx 2)`

`8x + 12 = 9x + 6`

Now, subtract `color(red)(8x)` and `color(blue)(6)` from each side of the equation to solve for `x` while keeping the equation balanced:

`-color(red)(8x) + 8x + 12 - color(blue)(6) = -color(red)(8x) + 9x + 6 - color(blue)(6)`

`0 + 6 = (-color(red)(8) + 9)x + 0`

`6 = 1x`

`6 = x`

`x = 6`