Answer: one solution; x = 7
Step-by-step explanation:
This is an equation in just one variable, and that variable is not raised to a power, nor are we taking a root of it. So this is an equation in a single variable without exponents or roots.
Thus, there should be exactly one solution, a single real number, or no solution at all.
We can confirm that by finding the solution. We will either get a real number or we will get some sort of contradiction that makes the equation unsovable as it is written. {Like if we get down to an obviously false statement such as 7 = 2. That would mean there is no value of 'x' that makes the equation true. Because it is NEVER true. :) }
3(x-2) = 22 - x (Given)
3x - 6 = 22 - x (Distributive Property)
x + 3x - 6 = 22 - x + x (add 'x' to both sides; addition property of =)
4x - 6 = 22 (Combine like terms)
4x - 6 + 6 = 22 + 6 (add 6 to both sides; addition property of =)
4x + 0 = 28 (-6 + 6 = 0; definition of additive inverse)
4x = 28 (4x + 0 = 4; Zero is Identity Element for Addition)
x = 7 (Divide both sides by 4, a nonzero number; division propety of =)