Let's analyze the charges for both Grayson and Ian to determine when Grayson's charges are higher than Ian's.
### Step-by-Step Solution:
1. Define the Cost Equations:
- Grayson's charges: [tex]\( 35h + 35 \)[/tex]
- Here, Grayson charges [tex]$35 per hour plus a $[/tex]35 administration fee.
- Ian's charges: [tex]\( 45h + 15 \)[/tex]
- Ian charges [tex]$45 per hour plus a $[/tex]15 administration fee.
2. Set Up the Inequality:
- We want to find out when Grayson's charges are more than Ian's, so we set up the inequality:
[tex]\[
35h + 35 > 45h + 15
\][/tex]
3. Simplify the Inequality:
- First, subtract [tex]\(35h\)[/tex] from both sides to isolate the term with [tex]\(h\)[/tex] on one side:
[tex]\[
35h + 35 - 35h > 45h + 15 - 35h
\][/tex]
Simplifies to:
[tex]\[
35 > 10h + 15
\][/tex]
- Next, subtract 15 from both sides to further simplify:
[tex]\[
35 - 15 > 10h
\][/tex]
Simplifies to:
[tex]\[
20 > 10h
\][/tex]
4. Solve for [tex]\(h\)[/tex]:
- To isolate [tex]\(h\)[/tex], divide both sides of the inequality by 10:
[tex]\[
\frac{20}{10} > h
\][/tex]
Simplifies to:
[tex]\[
2 > h
\][/tex]
Which can also be written as:
[tex]\[
h < 2
\][/tex]
### Conclusion:
Grayson charges more than Ian when the number of hours of tax preparation is less than 2 hours.
Thus, the correct answer is:
[tex]\[
\boxed{h < 2}
\][/tex]
