To find the value of [tex]\( x \)[/tex] given Carly's tutoring earnings, we can follow these steps:
1. Identify the rates and total earnings:
- Carly earns \[tex]$15 for each thirty-minute session.
- Carly earns \$[/tex]25 for each sixty-minute session.
- Her total earnings for the weekend were \$230.
2. Translate the problem into an equation:
- Let [tex]\( x \)[/tex] be the number of thirty-minute sessions.
- Since she had [tex]\( x - 2 \)[/tex] sixty-minute sessions, the income from these sessions is [tex]\( 25(x - 2) \)[/tex].
3. Set up the equation for the total earnings:
- Total earnings from thirty-minute sessions: [tex]\( 15x \)[/tex]
- Total earnings from sixty-minute sessions: [tex]\( 25(x - 2) \)[/tex]
- Combined total earnings: [tex]\( 15x + 25(x - 2) = 230 \)[/tex]
4. Simplify and solve the equation:
[tex]\[
15x + 25(x - 2) = 230
\][/tex]
[tex]\[
15x + 25x - 50 = 230
\][/tex]
[tex]\[
40x - 50 = 230
\][/tex]
[tex]\[
40x = 230 + 50
\][/tex]
[tex]\[
40x = 280
\][/tex]
[tex]\[
x = 7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{7} \)[/tex].
So, the correct answer is:
D. [tex]\( 7 \)[/tex]
