(8) Lesson 2.2 - Solve Two-Step Equations

(8) Lesson 2.2 - Solve Two-Step Equations

1. Course 3, Lesson 2-2 Solve each equation. Check your solution . 1. = 6 2. 0.6y = − 12 3. = 4. 8.6n = − 365.5 5. For art class, each student is going to make a pi ñata using pound of paste. The art teacher bought 20 pounds of paste. Write and solve an equation that can be used to determine the number of students that can make a pi ñata.

2. Course 3, Lesson 2-2 Answers 1. 8 2. − 20 3. 9 4. − 42.5 5. ; n = 25

3. WHAT is equivalence? Expressions and Equations Course 3, Lesson 2-2

4. 8.EE.7 Solve linear equations in one variable. 8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a , a = a , or a = b results (where a and b are different numbers). 8.EE.7b S olve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms . Course 3, Lesson 2-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations

5. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. Course 3, Lesson 2-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations

6. To identify the Properties of Equality solve two-step equations Course 3, Lesson 2-2 Expressions and Equations

7. properties two-step equation Course 3, Lesson 2-2 Expressions and Equations

8. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 1. Solve 2 x + 3 = 7. There are two 1-tiles in each group, so x = 2. Write the equation. Subtraction Property of Equality Division Property of Equality Remove three 1-tiles from each mat. Separate the remaining tiles into 2 equal groups. Using either method, the solution is 2. 7 Use a model. 2 x + 3 – 3 = 7 – 3 2 x = 4 Use symbols. 2 x + 3 = 7 Simplify. x = 2. – 3 = –3 2 x = 4

9. Answer Need Another Example? Solve 5 y + 1 = 26. 5

10. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 2. Solve 25 = n – 3. Write the equation. Addition Property of Equality Multiplication Property of Equality 25 = n – 3 28 = n The solution is 112. 112 = n Simplify. +3 = +3

11. Answer Need Another Example? –18 Solve –4 = z + 2.

12. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 3. Solve 6 – 3 x = 21. Write the equation. Subtraction Property of Equality Simplify. –3 x = 15 The solution is –5. Simplify. Rewrite the left side as addition. 6 – 3 x = 21 6 + (–3 x ) = 21 x = –5 Division Property of Equality Check 6 – 3 x = 21 Write the equation. Replace x with –5. 7 6 – 3 (–5) = 21 ? 6 – (–15) = 21 ? Multiply. 6 +15 = 21 ? To subtract a negative number, add its opposite. 21 = 21 The sentence is true. –6 = –6

13. Answer Need Another Example? Solve 8 – 3 x = 14. –2

14. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 4. Chicago’s lowest recorded temperature in degrees Fahrenheit is –27°. Solve the equation –27 = 1.8 C + 32 to convert to degrees Celsius. Write the equation. Division Property of Equality –32.8 ≈ C Simplify. Subtraction Property of Equality –27 = 1.8 C + 32 Simplify. Check the solution. So, Chicago’s lowest recorded temperature is about –32.8 degrees Celsius. –32 = –32 –59 = 1.8 C

15. Answer Need Another Example? Melisa wants to put trim molding around a rectangular table. The table is 45 inches long and she has 150 inches of trim. Solve the equation 150 = 2 w + 90 to find the width of the table. 30 in.

16. How did what you learned today help you answer the WHAT is equivalence? Course 3, Lesson 2-2 Expressions and Equations

17. How did what you learned today help you answer the WHAT is equivalence? Course 3, Lesson 2-2 Expressions and Equations Sample answers: In order to maintain the equality, when you perform an operation on one side of an equation, you must perform the same operation on the other side of the equation. Equations are equivalent when they have the same solution.

18. Write a two-step equation and explain how to solve it. Ratios and Proportional Relationships Expressions and Equations Course 3, Lesson 2-2