Unit 3 Day 5

1. Unit 3 Day 5

2. Solving Equations with the Variable on Each Side Common Core State Standards A.REI.1 Explain each step in solving a simple equations as following form the equality of numbers asserted at the previous step, starting fr0m the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Mathematical Practices 1. Make sense of problems and persevere in solving them. 5. Use appropriate tools strategically.

3. Variables on Each Side • To solve an equation that has variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variable on one side.

4. Example 1 • Solve an Equation with Variables on Each Side Solve . Check your solution.

5. Guided Practice • Solve each equation. Check your solution. 1A. 1B.

6. Guided Practice • Solve each equation. Check your solution. 1C. 1D.

7. Grouping Symbols • If equations contain grouping symbols such as parentheses or brackets, use the Distributive Property first to remove the grouping symbols.

8. Example 2 • Solve an Equation with Grouping Symbols Solve .

9. Guided Practice • Solve each equation. Check your solution. 2A. 2B.

10. Some equations may have no solution. That is, there is no value of the variable that will result in a true equation. Some equations are true for all values of the variables. These are called identities.

11. Example 3 • Find Special Solutions Solve each equation. a.

12. Example 3 • Find Special Solutions Solve each equation. b.

13. Guided Practice 3A.

14. Guided Practice 3B.

15. Summary Steps for Solving Equations • STEP 1 Simplify the expressions on each side. Use the Distributive Property as needed. • STEP 2 Use the Addition and/or Subtraction Property of Equality to get the variables on one side and the numbers without variables on the other side. Simplify. • STEP 3 Use the Multiplication or Division Property of Equality to solve.

16. Example 4 • Write an equation. Find the value of x so that the figures have the same area. 10 cm 6 cm 3 cm x cm x cm

17. Guided Practice • Find the value of x so that the figures have the same perimeter. 2x +2 x 6 x

18. Check For Understanding • Determine whether each solution is correct. If the solution is not correct, find the error and give the correct solution. 2 2

19. Check For Understanding • Determine whether each solution is correct. If the solution is not correct, find the error and give the correct solution. b. 3d = 3 3 d =

20. Check For Understanding • Determine whether each solution is correct. If the solution is not correct, find the error and give the correct solution. c. 13 = z

21. Check for Understanding • Solve each equation. 2. 3. 4. 5. 6. 7.

22. Check for Understanding • Solve each equation. 2. 3. 4 3 4. 5. no solution 6. 7. all real numbers 2.5

23. Solving Equations Involving Absolute Value Common Core State Standards A.REI.1 Explain each step in solving a simple equations as following form the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Mathematical Practices 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

24. Absolute Value Expressions • Expressions with absolute values define an upper and lower range in which a value must lie. Expressions involving absolute value can be evaluated using the given value for the variable.

25. Example 1 • Expressions with Absolute Value Evaluate if m = 4.

26. Guided Practice • Evaluateifx = 2.

27. Absolute Value Equations • There are three types of open sentences involving absolute value, , and . In this lesson, we will consider only the first type. Look at the equation . This means that the distance between 0 and x is 4. If , then or . Thus, the solution set is

28. Absolute Value Equations • For each absolute value equation, we must consider both cases. To solve an absolute value equation, first isolate the absolute value on one side of the equals sign if it is not already by itself.

29. Key Concept:Absolute Value Equations • Words When solving equations that involve absolute values, there are two cases to consider. • Case 1 The expression inside the absolute value symbol is positive or zero. • Case 2 The expression inside the absolute value symbol is negative. • Symbols For any real numbers a and b, if and , then or . • Example , so or

30. Example 2 • Solve Absolute Value Equations Solve each equation. a. =17 b.

31. Guided Practice 2A. 2B.

32. Real-World Example 3 • Solve an Absolute Value Equation SNAKES The temperature of an enclosure for a pet snake should be about 80F, give or take 5. Find the maximum and minimum temperatures.

33. Guided Practice • ICE CREAM Ice Cream should be stored at 5F with an allowance for 5. Write and solve an equation to find the maximum and minimum temperatures at which the ice cream should be stored.

34. Check For Understanding • Example 1 – Evaluate each expression if f = 3, g = , and h =5. 1. 2. 3.

35. Check For Understanding • Example 1 – Evaluate each expression if f = 3, g = , and h =5. 1. 2. 3. 15 11

36. Check For Understanding • Example 2 – Solve each equation. 4. 5. 6. 6 7. 8. 9.

37. Check For Understanding • Example 2 – Solve each equation. 4. 5. 6. 6 7. 8. 9.