How many solutions does each of the following equations have?
$4(x-3)=4x-12$

• A. One solution
• B. Infinite solutions
• C. No solution

Answer: (B)

Verified step by step guidance

1. Start by expanding the left side of the equation \(4\left(x - 3\right) = 4x - 12\) using the distributive property: multiply 4 by each term inside the parentheses.
2. After distributing, rewrite the equation as \$4x - 12 = 4x - 12$.
3. Next, observe both sides of the equation. Notice that the expressions on both sides are identical.
4. Since both sides are the same for all values of \(x\), this means the equation is true for every real number \(x\).
5. Therefore, the equation has infinitely many solutions because any value of \(x\) satisfies it.