Question

How do you solve `x/4+9=x/2-4`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(4)` to eliminate the fractions. `color(red)(4)` is used because it is the Lowest Common Denominator for both fractions:

`color(red)(4)(x/4 + 9) = color(red)(4)(x/2 - 4)`

`(color(red)(4) xx x/4) + (color(red)(4) xx 9) = (color(red)(4) xx x/2) - (color(red)(4) xx 4)`

`(color(red)(4)x)/4 + 36 = (color(red)(4)x)/2) - 16`

`color(red)(4)/4x + 36 = color(red)(4)/2x - 16`

`1x + 36 = 2x - 16`

Now, Subtract `color(red)(1x)` and add `color(blue)(16)` to each side of the equation to solve for `x` while keeping the equation balanced:

`1x - color(red)(1x) + 36 + color(blue)(16) = 2x - color(red)(1x) - 16 + color(blue)(16)`

`0 + 52 = (2 - color(red)(1))x - 0`

`52 = 1x`

`52 = x`

`x = 52`