Question

How do you solve `3a+13=9a-8`?

Answer 1

`a = 7/2`

Explanation:

First, isolate the `a` terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

`3a + 13 - color(red)(3a + 8) = 9a - 8 - color(red)(3a + 8)`

`3a - 3a + 13 + 8 = 9a - 3a - 8 + 8`

`0 + 13 + 8 = 9a - 3a - 0`

`13 + 8 = 9a - 3a`

Next, we can combine like terms:

`21 = (9 - 3)a`

`21 = 6a`

Now, solve for `a` while keeping the equation balanced:

`21/color(red)(6) = (6a)/color(red)(6)`

`(3 xx 7)/(3 xx 2) = (color(red)(cancel(color(black)(6)))a)/color(red)(cancel(color(black)(6)))`

`3/3 xx 7/2 = a`

`1 xx 7/2 = a`

`7/2 = a`