Question

You’re trying to find how many solutions the equation 3(x+12)=3x+4 has. Let’s start by getting rid of the parentheses. One way to do that is to divide both sides by the factor in front of the parentheses, 3. That step has been recorded for you. Now keep going. Divide both sides by 3 to rewrite the equation.
3x+12 = 3(x+4)
3 3
? = ?

Answer 1

To start, you've already divided both sides of the given equation \( 3(x + 12) = 3x + 4 \) by 3. The equation we have is:

\[
x + 12 = x + \frac{4}{3}
\]

Now, let's simplify this equation step by step:

1. Subtract \( x \) from both sides:

\[
12 = \frac{4}{3}
\]

This simplification shows that \( 12 \) is equal to \( \frac{4}{3} \), which is not true. Since we arrived at a false statement, this means the original equation has no solution.

Thus, the equation \( 3(x + 12) = 3x + 4 \) has **no solutions**.