Question

How do you solve `x+ \frac { 1} { 2} x = 15`?

Answer 1

`x = 10`

Explanation:

First, multiply each side of the equation by `color(red)(2)` to eliminate the fraction and keep the equation balanced. Eliminating the fraction will make the equation easier to work with:

`color(red)(2)(x + 1/2x) = color(red)(2) * 15`

`2x + 1x = 30`

We can now combine the `x` terms:

`(2 + 1)x = 30`

`3x = 30`

Finally we can solve for `x` while keeping the equation balanced by dividing each side of the equation by `3`:

`(3x)/color(red)(3) = 30/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 10`

`x = 10`

Answer 2

You may have seen the answer right away:

Explanation:

`1 1/2 x=1 1/2 xx10->x+10`

But if you haven't, here's the long way:

`->3/2x=15-> cancel2xx3/cancel2x=2xx15`

`->3x=30->x=30/3=10`