Expressions Equations and Inequalities 1. Bailey withdrew $135 from her checking account. Write an algebraic expression that describes Bailey’s action. Part I: If x represents the variable in the word problem above, explain what the variable should represent. (1 point) x = _____________________________________ Part II: Write an algebraic expression to model the situation. (2 points) Part III: Bailey works part-time at a movie theater. The theater pays employees an hourly wage based on their length of employment. Write an algebraic expression that describes how much Bailey’s employer pays part-time workers. (3 points) Length of employment (months) Hourly wage (dollars/hour) 6 7.55 12 7.85 18 8.15 24 8.45 2. Solve the equation with parentheses and variables on both sides of the equal sign. Part I: Use the distributive property to remove the parentheses. (1 point) Part II: Collect any like terms on both sides of the equation. (1 point) Part III: Bring all variable terms to one side of the equation. (Hint: Add x to both sides.) (1 point) Part IV: Bring all the constant terms to one side. A constant term is a number without a variable. (Hint: Subtract 1 from both sides.) (1 point) Part V: Now solve the one-step equation. Show your work. (1 point) 3. Ben has a part-time job at the Fun Station. Suppose he worked 13.5 hours last week and made $81. How much does Ben earn per hour? Step 1: Write an equation you can use to solve the problem. Be sure to define the variable. (3 points) Step 2: Solve the equation you wrote in step 1. (1 point with work shown) Step 3: Explain the meaning of the solution found in step 2. (1 point) 4. A semi-trailer truck stops at a weigh station before crossing over a bridge. The weight limit on the bridge is 75,500 pounds. The cab (front) of the truck weighs 22,150 pounds, and the trailer (back) of the truck weighs 11,300 pounds when empty. In pounds, how much cargo can the truck carry and still be allowed to cross the bridge? Part I: Write an equation or inequality that models this situation. Let c be the cargo weight. Show your work. (2 points) Part II: Solve the equation or inequality you wrote in Part I for c. What does this tell you about how much cargo the truck can carry and still be allowed to cross the bridge? (4 points) 5. Part I: Solve 7x − 6 > 8 and 3x + 4 ≥ 22 for x. (2 points) Part II: Graph the solution from Part I on the number line provided. Describe the solution in words. (2 points) 6. Solve and graph the compound inequality: 5c + 3 < 28 or –4c – 2 ≤ 14 Part I: Solve 5c + 3 < 28 or –4c – 2 ≤ 14 for c. (2 points) Part II: Graph the solution from Part I on the number line provided. Describe the solution in words. (2 points) 7. Mr. Nelson is checking some of the school’s sport balls to make sure they are in good shape and properly inflated. Use the table of recommended air pressures to define the ranges for properly inflated balls. Ball Average recommended psi (pounds per square inch) Tolerance Soccer ball 12.05 ±3.55 Basketball 8.00 ±0.5 Volleyball 4.44 ±0.18 Part I: Write an absolute value inequality for the recommended air pressure range for each type of ball. Use the variable x for the ball’s actual air pressure. (3 points) Soccer ball: Basketball: Volleyball: Part II: Choose one type of ball and write an absolute value inequality describing the air pressure of balls outside the recommended range. (1 point) Part III: What is the appropriate range for air pressure for the type of ball you selected in Part II? Hint: Look back at your answers to Part 1 to choose the absolute value inequality to solve. (3 points) 8. Thad and his four family members are going to the fair.