Grade 11 Math: Inequality Word Problems
Solve real-world problems by setting up and solving linear and quadratic inequalities. This worksheet covers various applications of inequalities.
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Inequality Word Problems
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Read each word problem carefully. Set up an inequality to represent the situation, solve it, and graph the solution on a number line where applicable. Show all your work.
1. A store sells T-shirts for $15 each. They need to sell enough T-shirts to cover their monthly expenses of $1200. How many T-shirts, x, must they sell to make a profit?
Graph your solution on the number line below:
2. Sarah wants to save at least $500 for a new laptop. She currently has $150 and saves $35 per week. How many weeks, w, will it take her to save enough money?
3. The ideal temperature for a certain chemical reaction is between 25°C and 35°C, inclusive. Write a compound inequality to represent the ideal temperature, T, and graph it on the number line.
4. A projectile is launched upward from a platform 10 meters high with an initial velocity of 20 m/s. Its height h (in meters) after t seconds is given by the equation h(t) = -5t^2 + 20t + 10. During what time interval is the projectile at a height of at least 25 meters?
5. A company manufactures smartwatches. The cost C (in dollars) to produce x smartwatches is C = 50x + 1000. The revenue R (in dollars) from selling x smartwatches is R = 150x. The company wants to make a profit of at least $2000. Which inequality represents this situation?
150x - (50x + 1000) > 2000
150x - 50x + 1000 >= 2000
150x - (50x + 1000) >= 2000
150x + 50x - 1000 >= 2000
6. If a business wants to maximize its profit, it should ensure its revenue is than its cost.
7. When solving an inequality, if you multiply or divide both sides by a negative number, you must the inequality sign.