When solving for a variable in algebra, isolate the variable on one side and everything else opposite to that variable.
You isolate the variable by undoing everything that is being done to that variable.
For example, if we have the equation x - 10 = 35 then the variable x is being subtracted by 10. We will need to reverse that operation.
We reverse subtraction by using the inverse of subtraction. The inverse of subtraction is addition.
And remember. Any operation we do on one side of the equation, we must also do on the other side.
x - 10 = 35
Add 10 to each side of the equation.
x - 10 + 10 = 35 + 10 x = 45
Now we now that is equal to 45.
50 = -6x + 4x - 8
What can we do here? Well, we can first combine like terms.
Combining like terms is the processing of adding any terms that are like. And like terms are terms that have the same variable(s) or lack of variables and exponents.
Some examples.
2x + 5x
The terms have both the x variables and have the same exponent. The exponent is not shown because anything to the first power is the same.
3 + 4
These terms have no variables and are to the same exponent. So, they can be added together.
The two like terms I see in the equation 50 = -6x + 4x - 8 are -6x and 4x. They both have the same variable and exponents.
50 = -6x + 4x - 8
Combine like terms.
50 = -2x - 8
Now the variable x is being multiplied by -2 and subtracted by 8.
We will need to reverse all of those operations. First reverse the subtract operation. Which can be done by adding both sides by 8.
50 = -2x - 8
Add both sides by 8.
50 + 8 = -2x - 8 + 8
58 = -2x
We are almost done.
Done the variable x is only being multiplied by -2. How can we reverse the multiplication operation? By division of course.
