Question

how many solutions exist for the given equation?

(3(x - 2) = 22 - x)

• zero
• one
• two
• infinitely many

Explanation:

Expand the left side of the equation

$$ 3(x - 2) = 22 - x $$

$$ 3x - 6 = 22 - x $$

Isolate the variable terms

$$ 3x + x = 22 + 6 $$

$$ 4x = 28 $$

Solve for x and determine the number of solutions

$$ x = \frac{28}{4} = 7 $$

Since there is exactly one unique value of \(x\) that satisfies the equation, there is exactly one solution.

Answer:

• zero
• one (Correct answer)
• two
• infinitely many