Sure, let's determine the value of [tex]\( x \)[/tex] step by step:
1. Identify the earnings for each session:
- Carly earns \[tex]$15 for each 30-minute session.
- Carly earns \$[/tex]25 for each 60-minute session.
2. Set up the total earnings equation:
- Let [tex]\( x \)[/tex] be the number of 30-minute sessions Carly had.
- Thus, she had [tex]\( x - 2 \)[/tex] 60-minute sessions.
3. Formulate the earnings equation:
- The earnings from [tex]\( x \)[/tex] 30-minute sessions: [tex]\( 15x \)[/tex] dollars.
- The earnings from [tex]\( x - 2 \)[/tex] 60-minute sessions: [tex]\( 25(x-2) \)[/tex] dollars.
- The total earnings are given as \$230.
4. Set up the equation:
- The total amount Carly earned can be represented as:
[tex]\[
15x + 25(x - 2) = 230
\][/tex]
5. Simplify and solve for [tex]\( x \)[/tex]:
- Expand the equation:
[tex]\[
15x + 25x - 50 = 230
\][/tex]
- Combine like terms:
[tex]\[
40x - 50 = 230
\][/tex]
- Add 50 to both sides:
[tex]\[
40x = 280
\][/tex]
- Divide both sides by 40:
[tex]\[
x = 7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{7}
\][/tex]
