How to Solve Algebra
Equations
The following equation is set up to include the most common errors students make.
Read it each day for five days.
To "solve" an equation is to move things around until you get the x all by itself on one side of the equation.
Let's "solve" the following equation:
x – 3 = 4(x – 1)
Always work inside the brackets first. Multiply all the inside terms by the outside term. So now the equation becomes
x – 3 = 4x - 4
| 4 times x is 4x
4 times -1 is -4 |
Now we want to move the -3 to the other side. Always perform the opposite operation when moving a term from one side to the other. So by moving –3 to the other side of the equation it becomes +3.
x = 4x – 4 +3
Now, when we add 3 to –4, we get –1. So now we have
x = 4x – 1
Next we want to move the 4x. Do the opposite with 4x (which is really +4x). This gives us
x - 4x = -1
which becomes
-3x = -1
| 1x take away 4x is -3x |
Now we want to move the -3, so we must do the opposite of x multiplied by –3. (-3x is really x multiplied by -3.) So we do the opposite of multiplication: we divide each side by –3. Now we have
x = -1 divided by -3 which is expressed as
| x = |
|
Because we have a minus sign in both the numerator and denominator of this fraction, we can cancel out the minus sign. So we have:
x = ⅓
We have "solved" the equation.
This also means that if we substitute 1/3 for x in the equation, we will get 1/3 = 1/3. You can see if your answer is correct by substituting. Remember this for tests.
