Question

How do you solve `(7/9)x-1/2=3`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(18)` to eliminate the fractions while keeping the equation balanced. Eliminating the fractions up front will make the problem easier to work with and `color(red)(18)` is the least common denominator of the two fractions:

`color(red)(18)((7/9)x - 1/2) = color(red)(18) xx 3`

`(color(red)(18) xx (7/9)x) - (color(red)(18) xx 1/2) = 54`

`(cancel(color(red)(18))2 xx (7/color(red)(cancel(color(black)(9))))x) - (cancel(color(red)(18))9 xx 1/color(red)(cancel(color(black)(2)))) = 54`

`14x - 9 = 54`

Next, add `color(red)(9)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`14x - 9 + color(red)(9) = 54 + color(red)(9)`

`14x - 0 = 63`

`14x = 63`

Now, divide each side of the equation by `color(red)(14)` to solve for `x` while keeping the equation balanced:

`(14x)/color(red)(14) = 63/color(red)(14)`

`(color(red)(cancel(color(black)(14)))x)/cancel(color(red)(14)) = (7 xx 9)/(7 xx 2)`

`x = (color(red)(cancel(color(black)(7))) xx 9)/(color(red)(cancel(color(black)(7))) xx 2)`

`x = 9/2`