Question

how many solutions exist for the given equation?

(12x + 1 = 3(4x + 1) - 2)

• zero
• one
• two
• infinitely many

Explanation:

Expand the right side of the equation

$$ 12x + 1 = 3(4x + 1) - 2 $$

$$ 12x + 1 = 12x + 3 - 2 $$

Simplify the constant terms

$$ 12x + 1 = 12x + 1 $$

Analyze the resulting identity

$$ 12x + 1 = 12x + 1 \implies 0 = 0 $$

Answer:

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