Let's break down the problem step by step to find the correct inequality to determine how many times Jimmy visited the student's home.
1. Identify the Fixed and Variable Charges:
- Jimmy charges a fixed amount of \[tex]$40 per semester for tutoring.
- In addition to the fixed charge, he charges an extra \$[/tex]10 for each home visit. Let [tex]\( x \)[/tex] represent the number of home visits.
2. Establish the Total Earnings:
- The total amount Jimmy earns from tutoring one student would be the sum of the fixed semester charge and the additional charge for home visits.
- Hence, the total earnings can be represented by the expression: [tex]\( 40 + 10x \)[/tex].
3. Set Up the Inequality:
- Jimmy made less than \[tex]$80 this semester from tutoring one student.
- So, the total earnings should be less than \$[/tex]80.
4. Formulate the Inequality:
- The inequality to represent this situation is: [tex]\( 40 + 10x < 80 \)[/tex].
Therefore, the correct inequality to determine how many times Jimmy visited the student's home is:
B. [tex]\( 40 + 10x < 80 \)[/tex]
Based on the detailed breakdown, this inequality correctly represents the scenario described in the problem.
