Let's analyze each step carefully to identify the mistake in solving the equation:
Given equation:
[tex]\[6x - 1 = -2x + 9\][/tex]
Step 1: Isolate the variable terms on one side of the equation.
[tex]\[6x - 1 + 2x = -2x + 2x + 9\][/tex]
This simplifies to:
[tex]\[8x - 1 = 9\][/tex]
So, up to this point, the operations are correct.
Step 2: Move the constant term to the other side of the equation.
[tex]\[8x - 1 + 1 = 9 + 1\][/tex]
This simplifies to:
[tex]\[8x = 10\][/tex]
Again, this is correct.
Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 8.
[tex]\[x = \frac{10}{8}\][/tex]
Here, the proper division gives us:
[tex]\[x = \frac{5}{4} \text{ or } 1.25\][/tex]
But the given steps showed:
[tex]\[x = \frac{8}{10}\][/tex]
[tex]\[x = \frac{4}{5}\][/tex]
This is incorrect because the correct simplified result of 10/8 should be 5/4 or 1.25.
Thus, the mistake is in Step 3, where the incorrect simplification was applied. The correct step should be:
[tex]\[x = \frac{10}{8} \text{ or } \frac{5}{4} \text{ or } 1.25\][/tex]
Therefore, the correct answer is:
D. Step 3 is incorrect and should be [tex]\(x = \frac{10}{8}\)[/tex].
