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.
[tex]3x - 6 = 22 - x[/tex]
Second, since our goal is to get the variable on one side by itself, we can start by adding 6 to each side.
[tex]3x = 22 - x + 6[/tex]
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.
[tex]3x = 28 - x[/tex]
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.
[tex]3x + x = 28[/tex]
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.
[tex]4x = 28[/tex]
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.
[tex]x = \frac{28}{4} [/tex]
Seventh, ask yourself, what times 4 equals 28? Another way to look at 28/4 is ([tex]28 \div 4 [/tex] , anyway you put it, your answer should be 7. Now we know that there is only one solution for this problem.
[tex]x = 7[/tex]
Answer: [tex]\fbox {x = 7}[/tex]
