Final answer:
Alex is incorrect; the equation 3.2x-5=3.2(x-5) has no solutions, as simplifying both sides leads to the false statement -5 = -16, which shows there is no value for x that satisfies the equation.
Step-by-step explanation:
Alex's claim that the equation 3.2x-5=3.2(x-5) has infinitely many solutions is incorrect. To understand why, let's analyze the equation step-by-step.
On the right side of the equation, the expression 3.2(x-5) uses the distributive property of multiplication over addition, which means multiplying the 3.2 inside the parentheses by x and -5. Doing so, we get 3.2x - 16.
Now, let's simplify the original equation:
3.2x - 5 = 3.2x - 16
If we try to solve for x, we immediately encounter a contradiction. Subtracting 3.2x from both sides gives us:
-5 = -16,
which is a false statement. This tells us that there is no value of x that can make the original equation true; therefore, there are no solutions to this equation, rather than infinitely many solutions.