Assignment: Solve Inequalities with Multiplication and Division

Choose any three (3) of the following five problems to solve.

1. Players from the local Little League plans to hold a car wash as a fundraiser. If they charge $5 per car, how many cars do they need to wash to earn at least $250 dollars?

a. Write an inequality to represent this situation, using x to represent the number of cars the players need to wash.

b. Solve the inequality by isolating the variable. Show all work leading to your answer.

c. Graph the solution on the number line. Be sure to include number labels to show the values of x on the number line.

d. Write 1-2 sentences to explain what the solution to the inequality represents for this situation.

2. Manuel plans to withdraw a certain amount of money each month from his savings account to make payments on a bicycle. For how many months should he withdraw $10 from his savings account, if he wants to withdraw at most $100?

a. Write an inequality to represent this situation, using x to represent the number of months that Manuel needs to withdraw money from his account.

b. Solve the inequality by isolating the variable. Show all work leading to your answer.

c. Graph the solution on the number line. Be sure to include number labels to show the values of x on the number line.

d. Write 1-2 sentences to explain what the solution to the inequality represents for this situation.

3. In a city council election, 2,445 votes were cast for one of the candidates. If the candidate received at least one-third of the votes, how many voters voted in the election?

a. Write an inequality to represent this situation, using x to represent the number of voters that voted in the election.

b. Solve the inequality by isolating the variable. Show all work leading to your answer.

c. Graph the solution on the number line. Be sure to include number labels to show the values of x on the number line.

d. Write 1-2 sentences to explain what the solution to the inequality represents for this situation.

4. Janine has two important tests to study for. If she plans to divide her study time equally between both tests, how long should she spend studying for each test if she wants to study for at most 90 minutes?

a. Write an inequality to represent this situation, using x to represent the amount of time Janine should study for each test.

b. Solve the inequality by isolating the variable. Show all work leading to your answer.

c. Graph the solution on the number line. Be sure to include number labels to show the values of x on the number line.

d. Write 1-2 sentences to explain what the solution to the inequality represents for this situation.

5. A pet-sitter wants to advertise in several local newspapers. If the newspapers charge $20 per advertisement, how much will the pet-sitter have to spend if she wants to place at least four ads?

a. Write an inequality to represent this situation, using x to represent the total amount of money the pet-sitter spends on advertisements.

b. Solve the inequality by isolating the variable. Show all work leading to your answer.

c. Graph the solution on the number line. Be sure to include number labels to show the values of x on the number line.

d. Write 1-2 sentences to explain what the solution to the inequality represents for this situation.