Question

an airplane can seat up to 175 passengers. the airline has already sold 87 tickets for a flight on the airplane. which graph represents the solution to the inequality that finds the number of tickets the airline can still sell? 80 81 82 83 84 85 86 87 88 89 90 91 80 81 82 83 84 85 86 87 88 89 90 91 80 81 82 83 84 85 86 87 88 89 90 91 80 81 82 83 84 85 86 87 88 89 90 91

Explanation:

Step1: Define the variable

Let \( x \) be the number of tickets the airline can still sell.

Step2: Set up the inequality

The total number of tickets sold (already sold + still to sell) must be less than or equal to the maximum capacity of 175. The airline has already sold 87 tickets, so the inequality is \( 87 + x \leq 175 \).

Step3: Solve the inequality

Subtract 87 from both sides: \( x \leq 175 - 87 \), which simplifies to \( x \leq 88 \).

Step4: Analyze the number line graphs

We need a number line that shows all values of \( x \) (number of additional tickets) less than or equal to 88. A closed circle at 88 (since \( x \) can be equal to 88) and an arrow pointing to the left (for values less than 88). Looking at the options, the fourth graph (the one with a closed circle at 88 and arrow to the left, considering the labels 80, 81, ..., 91) matches this description. Wait, let's re - check the options:

• First graph: Arrow left, but maybe not the right range.
• Second graph: Open circle, which would be for \( < \) not \( \leq \), so incorrect.
• Third graph: Arrow right, open circle, incorrect.
• Fourth graph: Closed circle (since it's \( \leq 88 \)) and arrow left, which is correct as \( x \leq 88 \).

Answer:

The fourth number - line graph (the one with the closed circle at 88 and the arrow pointing to the left among the given options, with the number labels 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91)