Question

How do you solve `1/4x-5/2=-2`?

Answer 1

x=2

Explanation:

In order to solve for the unknown value x, it is important to do the following:

Move the `-5/2` on the other side of the equation. Remember to change the sign on the other side of the equation.

Reason: x value needs to stay on its own, because to solve the equation it is needed to solve for x and therefore it is possible to do it by solving first all the known values.

Now it should be present on the right side of the equation the following:
`-2+5/2`
In this second step, this side will be calculated and since there is `5/2`, it is important to find the Least Common Denominator, which in this case it is 2. ( -2 has as denominator 1, while 5 has as denominator 2, therefore in order to find the LCD, it will done `1*2= 2`).

Since we just calculated the LCD, it is possible to solve the expression:
`(-2*2+5)/2`
-2 has to be multiplied by two because, it is important to have the same denominator, while 5 will stay the same because it has already 2 as denominator.
Expression should end up with the following= `1/2`

The equation should be now:
`1/4x=1/2`

Now it is needed to multiply each side by 4, because we want to get rid of the `1/4`
`4*(1/4)x=(1/2)*4`

which is equal to: x=`4/2` and now it is possible to simplify by 2.
The result you will get is x=2.
In order to test the result, you can substitute the value of x with 2 and both sides of the equation should end up with:

                                           #-2=-2#