Question

How do you solve 3x+15=8x-24?

Answer 1

see explanation below for how to solve this problem:

Explanation:

First, add and subtract the necessary values from each side of the equation to isolate the `x` terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

`3x + 15 - color(red)(3x) + color(blue)(24) = 8x - 24- color(red)(3x) + color(blue)(24)`

Now group and combine like terms:

`3x - color(red)(3x) + 15 + color(blue)(24) = 8x - color(red)(3x) - 24 + color(blue)(24)`

`0 +15 + 24 = 8x - 3x - 0`

`39 = 5x`

Now, divide each side of the equation by `color(red)(5)` to solve for `x` and keep the equation balanced:

`39/color(red)(5) = (5x)/color(red)(5)`

`39/5 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))`

`39/5 = x`

`x = 39/5`

or

`x = 7.8`