Let's analyze the steps provided by Fiona and identify where the missing step should be.
Given equation:
[tex]\[
\frac{1}{2} - \frac{1}{3}(6x - 3) = \frac{13}{2}
\][/tex]
Step 1: Use the distributive property to simplify
[tex]\[
\frac{1}{2} - 2x + 1 = \frac{13}{2}
\][/tex]
Now we need to combine like terms on the left-hand side:
[tex]\[
\frac{1}{2} + 1 = \frac{1}{2} + \frac{2}{2} = \frac{3}{2}
\][/tex]
So combining these, we get:
[tex]\[
\frac{3}{2} - 2x = \frac{13}{2}
\][/tex]
Step 2: Combine like terms, simplifying the equation to:
[tex]\[
\frac{3}{2} - 2x = \frac{13}{2}
\][/tex]
Then, we isolate the variable expression by using the addition property of equality:
[tex]\[
-2x = \frac{13}{2} - \frac{3}{2}
\][/tex]
[tex]\[
-2x = \frac{10}{2}
\][/tex]
[tex]\[
-2x = 5
\][/tex]
Step 3: Simplify by using the division property of equality:
[tex]\[
x = \frac{5}{-2} \div -2
\][/tex]
[tex]\[
x = \frac{5}{4}
\][/tex]
From our steps and detailed analysis, we see that the missing step in Fiona's solution is:
Simplify by combining like terms.
