Question

How do you solve `-\frac { 2} { u - 7} = - 8`?

Answer 1

See the entire solution process below: `u = 29/4`

Explanation:

First, multiply each side of the equation by `color(red)(u - 7)` to eliminate the fraction while keeping the equation balanced:

`color(red)(u - 7) * -2/(u - 7) = -8 * (color(red)(u - 7))`

`cancel(color(red)(u - 7)) * -2/color(red)(cancel(color(black)(u - 7))) = (-8 * color(red)(u)) + (-8 * color(red)(-7))`

`-2 = -8u + 56`

Next, subtract `color(red)(56)` from each side of the equation to isolate the `u` term while keeping the equation balanced:

`-2 - color(red)(56) = -8u + 56 - color(red)(56)`

`-58 = -8u + 0`

`-58 = -8u`

Now, divide each side of the equation by `color(red)(-8)` to solve for `u` while keeping the equation balanced:

`(-58)/color(red)(-8) = (-8u)/color(red)(-8)`

`(-2 * 29)/color(red)(-2 * 4) = (color(red)(cancel(color(black)(-8)))u)/cancel(color(red)(-8))`

`(color(red)(cancel(color(black)(-2))) * 29)/color(red)(color(black)(cancel(color(red)(-2))) * 4) = u`

`29/4 = u`

`u = 29/4`

Answer 2

`u=29/4`

Explanation:

`-2/(u-7)=-8`

Divide both sides by `-1`.

`2/(u-7)=8`

Multiply both sides by `(u - 7)` in order to get the variable out of the denominator.

`2=8(u-7)`

Then divide both sides by `8` in order to isolate `(u - 7)`.

`2/8=u-7`

Then add 7 to both sides to isolate `u`.

`7+2/8=u`

Then simplify to get:

`u=7+1/4=28/4+1/4=29/4`