Question

How do you solve `\frac { 4} { 3} u - \frac { 2} { 5} = - \frac { 7} { 5} u - 5`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(15)` to eliminate the fractions while keeping the equation balanced. `color(red)(15` is the common denominator for all of the fractions:

`color(red)(15)(4/3u - 2/5) = color(red)(15)(-7/5u - 5)`

`(color(red)(15) xx 4/3u) - (color(red)(15) xx 2/5) = (color(red)(15) xx -7/5u) - (color(red)(15) xx 5)`

`(cancel(color(red)(15))5 xx 4/color(red)(cancel(color(black)(3)))u) - (cancel(color(red)(15))3 xx 2/color(red)(cancel(color(black)(5)))) = (cancel(color(red)(15))3 xx -7/color(red)(cancel(color(black)(5)))u) - 75`

`20u - 6 = -21u - 75`

Next, add `color(red)(21u)` and `color(blue)(6)` to each side of the equation to isolate the `u` term while keeping the equation balanced:

`20u - 6 + color(red)(21u) + color(blue)(6) = -21u - 75 + color(red)(21u) + color(blue)(6)`

`20u + color(red)(21u) - 6 + color(blue)(6) = -21u + color(red)(21u) - 75 + color(blue)(6)`

`41u - 0 = 0 - 69`

`41u = -69`

Now, divide each side of the equation by `color(red)(41)` to solve for `u` while keeping the equation balanced:

`(41u)/color(red)(41) = -69/color(red)(41)`

`(color(red)(cancel(color(black)(41)))u)/cancel(color(red)(41)) = -69/41`

`u -69/41`