3(x – 2) = 22 – x
how many solutions exist for the equation?

3(x - 2) = 22 - x

First, we need to expand the problem (remove parentheses). The 3 outside will need to multiply into each term inside the parentheses. 


Second, since our goal is to get the variable on one side by itself, we can start by adding 6 to each side. 


Third, now we need to simplify the right side of the problem. 22 - x + 6, don't look at the variable in between the 22 and 6, and just add those two numbers. This will allow the solution to 22 + 6 to be subtracted to x.


Fourth, knowing that we have to get the variable (x) by itself on one side, we can continue by adding 'x' to both sides, which will flip the problem around.


Fifth, we can simplify 3x + x now. Basically, the variable by itself is considered a (1). So, now we can look at it as 3x + 1, which equals 4x.


Sixth, still focusing on the goal of getting the variable by itself, we can remove the 4 from the x by dividing both sides by 4. This will create a fraction.


Seventh, ask yourself, what times 4 equals 28? Another way to look at 28/4 is ( , anyway you put it, your answer should be 7. Now we know that there is only one solution for this problem.