* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Holt CA Course 1
Survey
Document related concepts
Transcript
11-3 Solving Multi-Step Equations Preview Warm Up California Standards Lesson Presentation Holt CA Course 1 11-3 Solving Multi-Step Equations Warm Up Solve. 1. –8p – 8 = 56 p = –8 2. 13d – 5 = 60 d=5 3. 9x + 24 = 60 x=4 4. k + 4 = 11 7 k = 49 5. 19 + z4 = 24 Holt CA Course 1 z = 20 11-3 Solving Multi-Step Equations California Standards Preview of Grade 7 AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, and commutative) and justify the process used. Also covered: Preview of Algebra 1 5.0 Holt CA Course 1 11-3 Solving Multi-Step Equations Remember! The Distributive Property states that a(b + c) = ab + ac. For instance, 2(3 + 5) = 2(3) + 2(5). Holt CA Course 1 11-3 Solving Multi-Step Equations You may need to use the Distributive Property to solve an equation that has parentheses. Multiply each term inside the parentheses by the factor that is outside the parentheses. Then combine like terms. Holt CA Course 1 11-3 Solving Multi-Step Equations Additional Example 1: Combining Like Terms to Solve Equations Solve 12 – 7b + 10b = 18. 12 – 7b + 10b = 18 12 + 3b = 18 – 12 – 12 3b = 6 3b = 6 3 3 b = Holt CA Course 1 2 Combine like terms. Subtract 12 from both sides. Divide both sides by 3. 11-3 Solving Multi-Step Equations Additional Example 2: Using the Distributive Property to Solve Equations Solve 5(y – 2) + 6 = 21. 5(y – 2) + 6 = 21 5(y) – 5(2) + 6 = 21 5y – 10 + 6 = 21 5y – 4 = 21 +4 5y 5 Holt CA Course 1 +4 = 25 5 y=5 Distribute 5 on the left side. Simplify. Combine like terms. Add 4 to both sides. Divide both sides by 5. 11-3 Solving Multi-Step Equations Additional Example 3: Problem Solving Application Troy has three times as many trading cards as Hillary. Subtracting 8 from the combined number of trading cards Troy and Hillary have gives the number of cards Sean has. If Sean owns 24 trading cards, how many trading cards does Hillary own? Holt CA Course 1 11-3 Solving Multi-Step Equations Additional Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. • Find the number of trading cards that Hillary owns. List the important information: • Troy owns 3 times as many trading cards as Hillary. • Subtracting 8 from the combined number of trading cards Troy and Hillary own gives the number cards Sean owns. • Sean owns 24 trading cards. Holt CA Course 1 11-3 Solving Multi-Step Equations Additional Example 3 Continued 2 Make a Plan Let c represent the number of trading cards Hillary owns. Then 3c represents the number Troy owns. Troy’s cards + Hillary’s cards – 8 = Sean’s cards 3c + c –8 = 24 Solve the equation 3c + c – 8 = 24 for c. Holt CA Course 1 11-3 Solving Multi-Step Equations Additional Example 3 Continued 3 Solve 3c + c – 8 = 24 4c – 8 = 24 +8 +8 4c Combine like terms. Add 8 to both sides. = 32 4c = 32 4 4 Divide both sides by 4. c=8 Hillary owns 8 cards. Holt CA Course 1 11-3 Solving Multi-Step Equations Additional Example 3 Continued 4 Look Back Make sure that your answer makes sense in the original problem. Hillary owns 8 cards. Troy owns 3(8) = 24 cards. Sean owns 24 + 8 – 8 = 24. Holt CA Course 1 11-3 Solving Multi-Step Equations Check It Out! Example 1 Solve 14 – 8b + 12b = 62. 14 – 8b + 12b = 62 14 + 4b = 62 – 14 – 14 4b = 48 4b = 48 4 4 b = Holt CA Course 1 12 Combine like terms. Subtract 14 from both sides. Divide both sides by 4. 11-3 Solving Multi-Step Equations Check It Out! Example 2 Solve 3(x – 3) + 4 = 28. 3(x – 3) + 4 = 28 3(x) – 3(3) + 4 = 28 3x – 9 + 4 = 28 Simplify. 3x – 5 = 28 Combine like terms. +5 +5 Add 5 to both sides. 3x 3 Holt CA Course 1 Distribute 3 on the left side. = 33 3 x = 11 Divide both sides by 3. 11-3 Solving Multi-Step Equations Check It Out! Example 3 John is twice as old as Hiro. Subtracting 4 from the combined age of John and Hiro gives William’s age. If William is 29, how old is Hiro? Holt CA Course 1 11-3 Solving Multi-Step Equations Check It Out! Example 3 Continued 1 Understand the Problem Rewrite the question as a statement. • Find Hiro’s age. List the important information: • John is 2 times as old as Hiro. • Subtracting 4 from the combined age of John and Hiro gives William’s age. • William is 29 years old. Holt CA Course 1 11-3 Solving Multi-Step Equations Check It Out! Example 3 Continued 2 Make a Plan Let h represent Hiro’s age. Then 2h represents John’s age. John’s age + Hiro’s age – 4 = William’s age 2h + h – 4 = 29 Solve the equation 2h + h – 4 = 29. Holt CA Course 1 11-3 Solving Multi-Step Equations Check It Out! Example 3 Continued 3 Solve 2h + h – 4 = 29 3h – 4 = 29 +4 +4 3h Combine like terms. Add 4 to both sides. = 33 3h = 33 3 3 Divide both sides by 3. h = 11 Hiro is 11 years old. Holt CA Course 1 11-3 Solving Multi-Step Equations Check It Out! Example 3 Continued 4 Look Back Make sure that your answer makes sense in the original problem. Hiro is 11 years old, then John is 2(11) = 22 years old. William is 22 + 11 – 4 = 29 years old. Holt CA Course 1 11-3 Solving Multi-Step Equations Solve. Lesson Quiz 1. c + 21 + 5c = 63 c=7 2. –x – 11 + 17x = 53 x=4 3. 59 = w – 16 + 4w 15 = w 4. 4(k – 3) + 1 = 33 k = 11 5. Kelly swam 4 times as many laps as Kathy. Adding 5 to the number of laps Kelly swam gives you the number of laps Julie swam. If Julie swam 9 laps, how many laps did Kathy swim? 1 lap Holt CA Course 1