Question

How do you solve `1/8x-3/4=7/16x+1/2`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(16)` to eliminate the fractions while keeping the equation balanced. `color(red)(16)` is the Lowest Common Denominator of all the fractions:

`color(red)(16)(1/8x - 3/4) = color(red)(16)(7/16x + 1/2)`

`(cancel(color(red)(16)) 2 xx 1/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(16)) 4 xx 3/color(red)(cancel(color(black)(4)))) = (cancel(color(red)(16)) xx 7/color(red)(cancel(color(black)(16)))x) + (cancel(color(red)(16)) 8 xx 1/color(red)(cancel(color(black)(2))))`

`2x - 12 = 7x + 8`

Next, subtract `color(red)(2x)` and `color(blue)(8)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(2x) + 2x - 12 - color(blue)(8) = -color(red)(2x) + 7x + 8 - color(blue)(8)`

`0 - 20 = (-color(red)(2) + 7)x + 0`

`-20 = 5x`

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

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

`-4 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))`

`-4 = x`

`x = -4`