How many solutions does the following equation have? \( 4(y-30)=4 y+12 \) Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

To solve the equation \( 4(y-30) = 4y + 12 \), first, distribute the 4 on the left side: \( 4y - 120 = 4y + 12 \). Next, subtract \( 4y \) from both sides: \( -120 = 12 \). Since this statement is obviously false, it indicates there are no values of \( y \) that can make the equation true. Therefore, the equation has (A) No solutions. Writing equations like this can often lead to false leads. A common mistake is to overlook the coefficients and focus solely on terms. One tip to avoid confusion is to simplify each side thoroughly before making comparisons, ensuring you don't jump to conclusions that can steer you away from the actual solution!