Question

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

Answer 1

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. 
$3x - 6 = 22 - x$

Second, since our goal is to get the variable on one side by itself, we can start by adding 6 to each side. 
$3x = 22 - x + 6$

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.
$3x = 28 - x$

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.
$3x + x = 28$

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.
$4x = 28$

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.
$x = \frac{28}{4}$

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

Answer: $\fbox {x = 7}$

Answer 2

Answer:

infinitely many

Step-by-step explanation: