To find the mistake in the given steps to solve the equation, let's review each step carefully:
1. Start with the original equation:
[tex]\(6x - 1 = -2x + 9\)[/tex]
2. Combine like terms by adding [tex]\(2x\)[/tex] to both sides:
[tex]\[
6x - 1 + 2x = -2x + 9 + 2x
\][/tex]
Simplifies to:
[tex]\[
8x - 1 = 9
\][/tex]
So, Step 2:
[tex]\[
8x - 1 = 9
\][/tex]
is correct.
3. Add 1 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
8x - 1 + 1 = 9 + 1
\][/tex]
Simplifies to:
[tex]\[
8x = 10
\][/tex]
So, Step 3:
[tex]\[
8x = 10
\][/tex]
is correct.
4. Divide both sides by 8 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{10}{8}
\][/tex]
Simplifies to:
[tex]\[
x = \frac{5}{4}
\][/tex]
which is equivalent to:
[tex]\[
x = 1.25
\][/tex]
However, in the given steps, the incorrect simplification was made from:
[tex]\[
x = \frac{8}{10}
\][/tex]
instead of the correct:
[tex]\[
x = \frac{10}{8}
\][/tex]
The mistake occurs due to the incorrect calculation in Step 3. It should have been:
[tex]\[
x = \frac{10}{8}
\][/tex]
The correct answer is:
B. Step 3 is incorrect and should be [tex]\(x=\frac{10}{8}\)[/tex].
