Question

6x+3 = 5(x+3)
You just performed balanced moves to try to isolate x, and ended up with x=12. How many solutions does this equation have?
6x + 3 = 5x + 15
−5x − 5x
x+3 = 15
x=12

Answer 1

Let's go through the given equation step by step to determine the number of solutions.

The equation you provided is:
\[ 6x + 3 = 5(x + 3) \]

First, let's expand the right side:
\[ 6x + 3 = 5x + 15 \]

Next, let's move all terms involving \( x \) to one side and constant terms to the other side:
\[ 6x - 5x = 15 - 3 \]
\[ x = 12 \]

We found a solution \( x = 12 \).

Now, let's assess how many solutions this equation has. Since we were able to isolate \( x \) and arrived at a single value, it indicates that the equation has exactly **one unique solution**.

To confirm, we can also check if substituting \( x = 12 \) back into the very original equation holds true:
\[ 6(12) + 3 = 5(12 + 3) \]
\[ 72 + 3 = 5(15) \]
\[ 75 = 75 \]

Since both sides of the equation are equal, \( x = 12 \) is indeed a solution.

Therefore, the equation \( 6x + 3 = 5(x + 3) \) has **one solution**: \( x = 12 \).