Question

How do you solve `\frac { 6( 7- z ) } { 5} = - z`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(5)` to eliminate the fraction while keeping the equation balanced:

`color(red)(5) xx (6(7 - z))/5 = color(red)(5) xx -z`

`cancel(color(red)(5)) xx (6(7 - z))/color(red)(cancel(color(black)(5))) = -5z`

`6(7 - z) = -5z`

Next, expand the terms in parenthesis on the left side of the equation.

`(6 xx 7) - (6 xx z) = -5z`

`42 - 6z = -5z`

Now, add `color(red)(6z)` to each side of the equation to solve for `z` while keeping the equation balanced:

`42 - 6z + color(red)(6z) = -5z + color(red)(6z)`

`42 - 0 = (-5 + 6)z`

`42 = 1z`

`z = 42`