Question

How do you solve `8x+15=3x-20`?

Answer 1

`x=-7`

Explanation:

show below

`8x+15=3x-20`

`8x-3x=-20-15`

`5x=-35`

`x=-7`

Answer 2

The solution to the equation is `x=-7`

Explanation:

Start by getting like terms on the same side of the equation, I'll subtract fifteen from both sides first:

`8x+15=3x-20`
`8x=3x-35`

Next, subtract `3x` from both sides:

`5x=-35`

And finally, divide by `5` on both sides.

`(color(red)(cancel(5))x)/color(red)(cancel(5))=(-35)/5`

The fives on the left cancel each other out (because `(5x)/5=x`), leaving us with this:

`x=(-35)/5`

`x=color(red)(-7)`

Answer 3

Re-arrange the equation, and you will find that `x=-7`

Explanation:

First, we'll add and subtract values from both sides such that all of the `x`-terms and their coefficients will end up on one side, and the constants will be on the other:

`8x+15color(red)(-3x)=cancel(3x)-20color(red)(cancel(-3x))`

`8xcolor(red)(-3x)+15=-20`

`5x+15=-20`

`5xcancel(+15)color(red)(cancel(-15))=-20color(red)(-15)`

`5x=-20color(red)(-15)`

`5x=-35`

Now that the equation has been rearranged as we like it, we'll divide both sides by `x`'s coefficient. In this expression, the coefficient is 5:

`(cancel(5)x)/color(red)(cancel(5))=(-35)/color(red)(5)`

`x=(-35)/color(red)(5)`

`color(green)(x=-7)`