Question

does the equation 6x + 3 = 5(x + 3) have one solution, no solutions, or infinitely many solutions?
6x + 3 = 5(x + 3)
6x + 3 = 5x + 15
-5x -5x
x + 3 = 15
x = 12
infinitely many solutions
one solution
no solutions

Explanation:

Step1: Expand right-hand side

$6x + 3 = 5x + 15$

Step2: Subtract $5x$ from both sides

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

Step3: Subtract 3 from both sides

$x + 3 - 3 = 15 - 3$
$x = 12$

Step4: Classify solution type

Since we found one unique value for $x$, the equation has one solution.

Answer:

One solution, $x=12$