How many solutions exist for the given equation?
3(x – 2) = 22 – x
zero
one
two
infinitely many

Option (b) is the correct answer.

Step-by-step explanation:

The given equation is as follows.

                    3(x – 2) = 22 – x

Open the brackets and then multiply as follows.

                      3x - 6 = 22 - x

Now, taking the variables on left side and constants on the right side as follows.

                      3x + x = 22 + 6

                      4x = 28

                       x =

Cancelling the fraction by common factors, we will get the value of x as follows.

                       x = 7

As there is only one value of x. Thus, we can conclude that there exists only one solution for the equation   3(x – 2) = 22 – x.