Question

How do you solve `\frac { 47} { 8} x + 17= 13x - 12`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(47/8x)` and add `color(red)(12)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`47/8x + 17 - color(red)(47/8x) + color(red)(12) = 13x - 12 - color(red)(47/8x) + color(red)(12)`

`47/8x - color(red)(47/8x) + 17 + color(red)(12) = 13x - color(red)(47/8x) - 12 + color(red)(12)`

`0 + 29 = (8/8 xx 13x) - color(red)(47/8x) - 0`

`29 = 104/8x - color(red)(47/8x)`

`29 = 57/8x`

Now, multiply each side of the equation by `color(red)(8/57)` to solve for `x` while keeping the equation balanced:

`color(red)(8/57) xx 29 = color(red)(8/57) xx 57/8x`

`232/57 = x`

`x = 232/57`