Question

How do you solve `8= - \frac { 7} { u - 4}`?

Answer 1

`u = 25/8 = 3 1/8`

Explanation:

`8 = -7/((u-4))`

The biggest problem is that the variable is in the denominator.

There is one term on each side of the equation, so you have two options:

1. Cross multiply

`8(u-4) = -7`

`8u -32 = -7`

`8u = 32-7`

`8u= 25`

`u = 25/8`

`u = 3 1/8`

2. Invert both sides

`8/1 = (-7)/(u-4)`

`1/8 = (u-4)/-7" "larr xx -7` on both sides

`-7/8 = u-4`

`4-7/8 =u`

`u = 3 1/8 = 25/8`

Answer 2

See a solution process below:

Explanation:

First, we can rewrite the equation as:

`8/1 = -7/(u - 4)`

Because both sides of the equations are stand alone fractions we can "flip" the fractions to write:

`1/8 = -(u - 4)/7`

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

`color(red)(-7) xx 1/8 = color(red)(-7) xx (u - 4)/(-7)`

`-7/8 = cancel(color(red)(-7)) xx (u - 4)/color(red)(cancel(color(black)(-7)))`

`-7/8 = u - 4`

Now, add `color(red)(4)` to each side of the equation to solve for `u` while keeping the equation balanced:

`-7/8 + color(red)(4) = u - 4 + color(red)(4)`

`-7/8 + (8/8 xx color(red)(4)) = u - 0`

`-7/8 + 32/8 = u`

`25/8 = u`

`u = 25/8`