Let's start by setting up the situation based on the given information:
1. Terrence spends 10 hours driving with an instructor.
2. Additionally, he attends 2-hour classes every week.
3. He needs to complete a total of 26 hours of instruction to be eligible to take his driver's test.
We are asked to find [tex]\( w \)[/tex], the number of weeks the driving classes will last.
First, let's look at the equations provided and determine which one correctly represents the situation:
- [tex]\(2w + 10 = 26\)[/tex]
- [tex]\(10(w + 2) = 26\)[/tex]
- [tex]\(10w + 2 = 26\)[/tex]
- [tex]\(2(w + 10) = 26\)[/tex]
To find the correct equation, note the following:
- The total number of hours Terrence spends with the instructor is 10 hours.
- Each week, Terrence attends an additional 2-hour class.
- We need to find the total number of hours as a sum of these activities.
The equation that correctly represents this sum should be:
[tex]\[
10 \text{ (hours with the instructor)} + 2w \text{ (2 hours for each week for w weeks)} = 26 \text{ (total hours)}
\][/tex]
This simplifies to:
[tex]\[
2w + 10 = 26
\][/tex]
Next, let's solve for [tex]\( w \)[/tex]:
1. Start with the equation:
[tex]\[
2w + 10 = 26
\][/tex]
2. Subtract 10 from both sides to isolate the term with [tex]\( w \)[/tex]:
[tex]\[
2w = 16
\][/tex]
3. Divide both sides by 2 to solve for [tex]\( w \)[/tex]:
[tex]\[
w = 8
\][/tex]
So, the number of weeks the driving classes last is [tex]\( 8 \)[/tex] weeks.
The correct equation is [tex]\(\boxed{2w + 10 = 26}\)[/tex], and the number of weeks [tex]\( w \)[/tex] is [tex]\(\boxed{8}\)[/tex] weeks.
