Single Variable:
Solving equations is a fine skill like learning how to play an instrument.  It takes time to develop your skills, starting with the basics of addition and multiplication to more advanced functions.  Education within the algebra world of solving equations starts with a simple 1 coefficient problem.  An Example would suffice:

24 – x = 12

Here we have 1 variable, -x, with 2 values on both sides of the equation.  The key is to isolate the variable to one side and everything else on the other side.
First, looking at this equation we can see that the only value preventing –x from being isolated is 24.  We move that value to the opposite side by subtracting in this case.

24- x =12
-x = 12 –24
-x = -12

Next we must fully isolate our x value by dividing by –1

-x= -12
-x/-1= -12 / -1
x= 12

And that’s it!  We have solved for the value of x to be 12 and we can plug that value into our original problem to verify our results.

24 – (12) = 12
12= 12   Perfect!



Multiple Variables:
Next, algebraic expression require to learn is solving for a variable with another variable located within our equation.  You wont have a set definite answer, just simply a value equation for the variable being solved.  For example :

- 4 =  6x – 10 + y
Solve for x

So again, we want to isolate our variable that we are attempting to solve for.  We must move both the –10 and the y variable to the other side.

-4 = 6x – 10 + y
-4 – y= 6x – 10
-4 – y + 10 = 6x

Finally divide EVERYTHING by 6 to completely isolate the x variable
-4 – y + 10 = 6x
(-4 – y + 10) / 6  = x

And that’s the answer! We have solved for x



Several Same Variable:
Tons of people need help solving equations with several of the same variable located within the same problem on both sides of the equation.  Here is an example problem:

-2(4c – 6) = 1/3 (-12c + 24)

There are a lot of things going on with this equation.
For this problem we will try to isolate the only variable, c, by combining both terms onto the same side of the equation. 

The first step is to execute the almighty distributive property.  We must distribute the –2 and the 1/3 with their respective parenthesis.

-2(4c – 6) = 1/3 (-12c + 24)
-8c + 12 = -4c + 8

Now the problem looks much more manageable.  Solving equations can be easy this way!
Next step is to move all of the c variable to one side.  For this problem I am going to move the –8c term to the other side

-8c + 12 = -4c + 8
12= 4c + 8

Now we must isolate the c variable by ridding the right side of the 8. 

12= 4c + 8
4= 4c

And divide by 4 to solve!

4 = 4c
c= 1

And so we test our answer by simply plugging it back into our equation and hopefully both sides equal each other!

-2( 4 x 1 - 6)  =  1/3 ( -12 x 1 + 24)
-2 (4 – 6) = 1/3 (-12   + 24)
-2 (-2)=  1/3 ( -12)
-4 = -4

Perfect!


There are many more advanced equations to learn, but these 3 are the basis of algebraic expressions.  Remember, practice makes perfect.  Furthermore, If you need help solving equations contact us!