Question

How do you evaluate `-\frac { 5} { u - 6} = \frac { 5} { 2u - 12} + 3`?

Answer 1

`u=7/2=3.5`

Explanation:

First, let's rearrange the equation.

`-5/(u-6)=5/(2u-12)+3 ->`

`3=5/(2u-12)+5/(u-6)`

Next, you need have the a common denominator for the right side of the equation. You can do this by multiplying `5/(u-6)` by `2/2`. Then simplify the right side of the equation.

`-3=5/(2u-12)+5/(u-6) ->`

`-3=5/(2u-12)+(2/2)(5/(u-6))`

`-3=5/(2u-12)+10/(2u-12) ->`

`-3=15/(2u-12)`

Now we can solve for u. There are two things you can do. One is to cross multiply. The other is to flip both sides of the equation to get the variable in the numerator. Whichever you do will bring you to the same. I will show both. First, will be cross multiplication. -3 can be expressed as `-3/1`. Then you can divide by 3 after cross multiplying to isolate the `2u+12`.

`-3=15/(2u-12) ->`

`-3/1=15/(2u-12) ->`

`-3(2u-12)=15*1 ->`

`2u-12=5`

The other way I mentioned was to flip the fractions. Let's try that. When you do this method, you can multiply both sides by 15 to isolate `2u+12`.

`-3=15/(2u-12) ->`

`-1/3=(2u-12)/15 ->`

`-5=2u-12`

As you can see, both ways give us `2u+12=5`. Now we can solve for u.

`2u-12=-5 ->`

`2u=7`

`u=7/2=3.5`

If you want to, you can check to make sure your answer makes sense.

`-5/(u-6)=5/(2u-12)+3 ->`

`-5/(7/2-6)=5/(2(7/2)-12)+3 ->`

`-5/(7/2-12/2)=5/(7-12)+3 ->`

`-5/(5/2)=5/-5+3 ->`

`2=-1+3`

`2=2` `sqrt`

Since this is a true statement, that means that the answer is correct.