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Mastering Equations and Inequalities: Simplifying Expressions and Word Problems

This resource focuses on simplifying algebraic expressions, solving equations, and tackling inequalities through real-world word problems. Students will learn how to identify the necessary variables, constants, and operations required to formulate equations or inequalities based on given situations. Examples include calculating hourly wages, budget constraints for car rentals, and sales targets. Perfect for enhancing algebra skills and preparing for assessments, this guide offers a clear explanation of processes and strategies for successful problem-solving.

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Mastering Equations and Inequalities: Simplifying Expressions and Word Problems

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  1. Warm-Up • Turn in HW Worksheet even if you have questions on some problems. Easy 100 grade. • Simplify • 9x – 3x • 24y + 2x + 4y • 35c – 30c2 • -8b + 3f – 9b – 2b + 5f • 3x2 -3x + x2 – 7 + x +2 6x 28y + 4x 35c – 30c2 -19b +8f 4x2 -2x -5

  2. Equations and Inequalities – Word Problems • Decide equation or inequality • Determine the variable and what it’s representing. • Determine the constant(s) in the word problem. • Determine the operation(s). • Write the equation/inequality. • Solve the equation/inequality.

  3. Example #1 • Brandon worked at Jack in the Box for 37.5 hours last week. His pay for the week, before taxes were deducted, was $346.88. How much did he earn per hour? • Equation or Inequality? • Variable? • Constants? • Operation? • Write Equation. • Solve Equation. Equation money earned per hour 37.5-hours; 346.88-paycheck multiply 37.5x = 346.88 x = 9.25

  4. Example #2 • The charge for a rental car is $0.10 per mile. Celeste is on a business trip and must rent a car to attend various meetings. She has a budget of $60. What is the greatest number of miles Celeste can travel without going over her budget? Equation or Inequality? Variable? Constants? Operation? Write Equation. Solve Equation. Inequality number of miles .10 per mile; 60-budget multiply .10x ≤ 60 x = 600

  5. Example #3 • Keaton sells bicycles. He makes $120 per week plus $10 for each bicycle sold. He earned $400 this week. How many bicycles did he sell? Equation or Inequality? Variable? Constants? Operation? Write Equation. Solve Equation. Equation Bicycles sold 120-week; 10-for each bicycle; 400-paycheck earned multiply and add 120 + 10x = 400 x = 28

  6. Own Your Own • Briana is a sales representative for an appliance distributor. She needs to make $5000 in weekly sales of a particular TV model to qualify for a sales competition to win a trip to the Bahamas. If each TV sells for $250, how many TVs will she have to sell to qualify? • Christopher, Anthony, Shawn, Ricky, Kacey, Jonathan, Cece, Austin, Pete, Ethan, and Harold all got the same grade on an Algebra Test. If their combined score was a 1,001, what grade did they each get?

  7. Last One—Maybe • The admission fee to a video game arcade is $1.25 per person, and it costs $0.50 for each game played. Alex, Gabe, Nico, and Aaron have a total of $10.00 to spend. What is the greatest number of games they will be able to play as a group?

  8. 3x

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