Question

does the equation $6x + 3 = 5(x + 3)$ have one solution, no solutions, or infinitely many solutions? what move could we make to get rid of the $5x$ term on one or the sides, while keeping the equation balanced?
$6x + 3 = 5(x + 3)$
$6x + 3 = 5x + 15$
options: add $5x$ to each side, subtract $5x$ from each side, multiply each side by $5x$

Explanation:

Step1: Expand right-hand side

$$6x + 3 = 5x + 15$$

Step2: Isolate x terms

Subtract $5x$ from both sides:
$$6x - 5x + 3 = 5x - 5x + 15$$
$$x + 3 = 15$$

Step3: Solve for x

Subtract 3 from both sides:
$$x + 3 - 3 = 15 - 3$$
$$x = 12$$

Step4: Identify solution count

There is one unique value for x.

Step5: Choose balancing move

To eliminate $5x$ on the right, subtract $5x$ from each side.

Answer:

The equation has one solution. The valid move to balance the equation is "Subtract 5x from each side".
The solution for $x$ is $\boldsymbol{12}$.