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

Oct 11, 2015

x=2

#### Explanation:

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

Move the $- \frac{5}{2}$ 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:
$- 2 + \frac{5}{2}$
In this second step, this side will be calculated and since there is $\frac{5}{2}$, 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 $1 \cdot 2 = 2$).

Since we just calculated the LCD, it is possible to solve the expression:
$\frac{- 2 \cdot 2 + 5}{2}$
-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= $\frac{1}{2}$

The equation should be now:
$\frac{1}{4} x = \frac{1}{2}$

Now it is needed to multiply each side by 4, because we want to get rid of the $\frac{1}{4}$
$4 \cdot \left(\frac{1}{4}\right) x = \left(\frac{1}{2}\right) \cdot 4$

which is equal to: x=$\frac{4}{2}$ 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