Report

U1-S3-L2 One-Step Inequalities Essential Question: How do you solve and graph one-step inequalities? RULES FOR INEQUALITIES 1) GOAL: Isolate the variable on ISOLATE one side of the inequality. 2) Always perform the same operation to both sides of an inequality to keep it balanced. BALANCE 3) To undo an operation, INVERSE perform its opposite operation OPERATION to both sides of the inequality. VOCABULARY & Key Concepts • Equivalent Inequalities: inequalities with the same solution set. • When multiplying or dividing by a negative number, you must reverse the inequality symbol to keep it true. Inequalities Inequalities Inequalities Set-Builder Notation One-Step Addition & Subtraction • Solve just like equations: use the inverse operation! Examples: 1) x + 9 < 15 2) d – 3 > -6 3) 0.7 > n – 0.4 The solutions of x + 9 < 15 are given by x < 6 Practice One-Step Multiplication & Division • Solve just like equations: use the inverse operation! • Examples: 1) 3x > -27 2) 2 r 6 3 Practice Negative Numbers One-Step Multiplication & Division • If the number with the variable is negative, you must reverse the inequality symbol when you do the inverse operation! • Examples: 1) -8x > 72 2) x 3 5 Practice • Solve each inequality and graph the solution. Check your answer. 2a. -12x > 84 2b. 8 x 3 2c. 4.25 > -0.25h Extension 1) Sami has a gift card. She has already used $14 of the of the total value, which was $30. Write, solve, and graph an inequality to show how much more she can spend. Answer 3 Solve g + 14 ≤ 30 – 14 – 14 g + 0 ≤ 16 Since 14 is added to g, subtract 14 from both sides to undo the addition. g ≤ 16 It is not reasonable for Sami to spend a negative amount of money, so graph numbers less than or equal to 16 and greater than 0. 0 2 4 6 8 10 12 14 16 18 10 Extension 2) A certain restaurant has room for 120 customers. On one night, there are 72 customers dining. Write and solve an inequality to show how many more people can eat at the restaurant. x + 72 ≤ 120; x ≤ 48, where x is a natural number Extension 3) A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible numbers of shirts she can buy? 0, 1, 2, 3, 4, 5, 6, or 7 shirts Check for Understanding 1) How is solving inequalities similar to solving equations? 2) How is the solution of an inequality different from the solution of an equation? Summary • Answer the essential questions in detailed, complete sentences. • How do you solve and graph one-step inequalities? • Write 3-5 study questions in the left column to correspond with the notes.