Linear Inequalities in One Variable
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| 1) Write an inequality for the following: 5 less than 2 times a number is greater than 7.
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| 2) Write and solve an inequality for the following: 6 more than the sum of a number and 4 is less than 25.
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| 3) Jacob wants to buy a new video game. Store A is selling the game online for 15% off plus free shipping. Store B is selling the game online for 30% off but charges 3.95 shipping. What would the regular price of the video game have to be for store A to have the better deal? Round to the nearest penny.
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| 4) What is the domain for problem #3?
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| 5) Josie can produce g number of gadgets each hour at her factory job. The boss would like her to make a minimum of 50 gadgets per hour. Write an inequality that represents this situation. Let x = the number of hours worked. |
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| 6) Mrs. Smith needs to purchase supplies for her new classroom. She purchases n notebooks and b binders for each student. If she buys over 100 items, she will get a discount. Write the inequality that represents this problem so that Mrs. Smith will get a discount on her purchase. Let x = the number of students.
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| 7) Juan’s boss has asked him to enter data for at least 60 spreadsheets. He has given him a deadline of 1 week (5 work days). Juan is already ahead because he completed 2 of them this past week before the boss made the deadline. How many spreadsheets will he need to complete each day to meet the deadline? Write the inequality that represents this problem.
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| 8) Malik wants to put down a tile border around his new pool. Due to the expense of the pool, he only has $600 left to spend. If tiles cost $5 each, what is the most number of tiles can he afford to purchase? Write the inequality.
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| 9) Solve the inequality for #8.
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| 10) Give the domain and range for the problem in #8.
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Linear Inequalities in Two Variables
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| 11) Robert is building model cars as well as model trains. The cars take 4 hours to build while the trains take 6 hours to build. He is hoping to build as many as possible before the next model fair exhibition. If he has 100 free hours until the fair, how many can he build? Write the inequality for this problem. Let cars be the domain and trains the range.
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| 12) Use the x-intercept and y-intercept to help you find the domain and range for this inequality (problem #11).
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| 13) Choose the correct graph for this inequality (problem #11).
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| 14) The high school is selling tickets to their musical. Adult tickets are $10 and students tickets are $8. The students spent $850 on supplies for the musical (things like costumes and scripts). Write an inequality that shows how many tickets they will need to sell to not only earn back the $850 but also make a profit to use for the next show. Let x = # of adult tickets and y = # student tickets.
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| 15) Fill in the following table of values for problem #14.
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| 16) Use the table from #15 to graph this inequality. You can do that at https://www.desmos.com/calculator. Then discern the domain and range for this problem.
Hint: Make sure you consider what types of numbers represent the number of tickets you can sell.
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| 17) Joanna is going shopping to buy purses and shoes to accessorize her new wardrobe. The store charges $30 for each pursue and $45 for each pair of shoes. Joanna has $300 to spend. Write an inequality relating the number of purses and pairs of shoes that she will be able to purchase.
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| 18) Graph this inequality. You can do this by hand and scan it or you can use an online calculator and take a screenshot and attach the screenshot. If you want to use a free online graphing calculator, go to : https://www.desmos.com/calculator. Use the link below to attach your graph.
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Review
Click here to review the unit content explanation for More on Quadratics.
Click here to review the unit content explanation for Rational Expressions.
Click here to review the unit content explanation for Operations with Radicals.
For the next two problems, solve each equation by "completing the square."
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| 19) Solve for “x.”
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| 20) Solve for “x.”
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| 21) Explain the solution to the previous problem.
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| 22) Solve the following equation using the quadratic formula.
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For the next two problems, find each sum or difference.
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| 23) Find the sum.
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| 24) Find the difference.
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For the next two problems, solve each equation.
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| 25) Solve for “y.”
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| 26) Solve for “z.”
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For the next four problems, simplify.
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| 27) Simplify.
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| 29) Simplify.
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| 30) Simplify.
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| 31) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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