Solutions to Inequalities

Open Ended

The solution to $$5-3x > 35$$ is either $$x>-10$$ or $$-10>x$$ . Which solution is correct? Explain how you know.

Open Ended

The school band director determined from past experience that if they charge $$t$$ dollars for a ticket to the concert, they can expect attendance of $$1000-50t$$ . The director used this model to figure out that the ticket price needs to be \$8 or greater in order for at least 600 to attend. Do you agree with this claim? Explain your reasoning.

Multiple Choice

The school marching band has a budget of up to $$750 to pay for 15 new uniforms and competition fees that total$$ 300. Which inequality represents this situation?

• 15x + 300 ≥ 750
• 10x + 300 ≤ 750
• 15x + 200 ≤ 750
• 15x + 300 ≤ 750

Multiple Choice

The school marching band has a budget of up to $$750 to pay for 15 new uniforms and competition fees that total$$ 300. Solve the inequality and describe what it means in the situation.

• The maximum cost per uniform is 30.
• The maximum cost per uniform is 20.
• The total budget for uniforms is 1000.
• The maximum cost per uniform is 50.