Based on the scenario in the image, here’s how we can form the inequality:

Given:

• $x$: Number of hours spent washing cars.
• $y$: Number of hours spent tutoring.
• $8x$: Income from washing cars at $8 per hour.
• $16y$: Income from tutoring at $16 per hour.
• Total income requirement: At least $160.

Inequality for earnings:

$8x + 16y \geq 160$

Additionally, Connor can work for a maximum of 14 hours in total: $x + y \leq 14$

Final set of inequalities:

1. $8x + 16y \geq 160$ (to meet income requirement)
2. $x + y \leq 14$ (to meet the time constraint)
3. $x \geq 0, y \geq 0$ (since negative hours don’t make sense).

Would you like help solving these inequalities or visualizing the solution set?

Related Questions:

1. How can we graph these inequalities?
2. What is the maximum possible income Connor can earn under these constraints?
3. If Connor works equal hours washing cars and tutoring, how many hours will he work, and what is his total income?
4. How many hours must he tutor at a minimum to meet the $160 requirement?
5. What happens if he wants to maximize his time tutoring instead of washing cars?

Tip:

Remember, dividing by coefficients like 8 and 16 can simplify these inequalities, but keep all terms aligned with the conditions!