1. Must show ALL steps and ALL work for credit Equations - Introduction

2. Vocabulary EquationSolution Inverse Operation Insert Lesson Title Here Course 2 1-10 Equations and Their Solutions

3. Ella has 22 CDs. This is 9 more than her friend Kay has. This situation can be written as an equation. An equation is a mathematical statement that two expressions are equal in value. An equation is like a balanced scale. Right expressionLeft expression Number of CDs Ella has 22 is equal to = 9 more than Kay has j + 9 Course 2 1-10 Equations and Their Solutions

4. Just as the weights on both sides of a balanced scale are exactly the same, the expressions on both sides of an equation represent exactly the same value. When an equation contains a variable, a value of the variable that makes the statement true is called a solution of the equation. 22 = j + 9 j = 13 is a solution because 22 = 13 + 9. 22 = j + 9 j = 15 is not a solution because 22  15 + 9. The symbol ≠ means “is not equal to.” Reading Math Course 2 1-10 Equations and Their Solutions

5. Determine whether the given value of the variable is a solution of t + 9 = 17. Additional Example 1A: Determining Whether a Number is a Solution of an Equation 26 26 + 9 = 17 ? 35 = 17 ? 26 is not a solution of t + 9 = 17.  Substitute 26 for t. t + 9 = 17 Course 2 1-10 Equations and Their Solutions

6. Additional Example 1B: Determining Whether a Number is a Solution of an Equation Determine whether the given value of the variable is a solution of t + 9 = 17. 8 8 + 9 = 17 ? 17 = 17 ? 8 is a solution of t + 9 = 17. Substitute 8 for t. t + 9 = 17 Course 2 1-10 Equations and Their Solutions

7. Learn to solve one-step equations. Sections 1.11 and 1.12 in textbook. Course 2 12-1 Solving Two-Step Equations

8. How to solve one-step equations 1. Goal – Get the variable alone 2. Use the inverse operation to undo On BOTH sides of the equation Addition and Subtraction are inverse operations Multiplication and Division are inverse operations **Remember – Whatever you do to one side you MUST do to the other side!!!

9. 2-Column Notes Example#1 b + 2 = 6 Step 1 -2 -2 Step 2 b = 4 Step 3 Check 4 + 2 = 6 Step 4 6 = 6 Step 5 Instructions – STEPS 1) Copy Problem 2) Inverse Operation on BOTH sides *Do the Math!!!! 3) Solution – Box –in 4) Check Answer Rewrite equation with Value substituted 5) Do Math and check BOTH sides

10. 2-Column Notes Example#2 n – 36 = 17 Step 1 +36 +36 Step 2 n = 53 Step 3 Check 53–36 = 17 Step 4 17 = 17 Step 5 Instructions – STEPS 1) Copy Problem 2) Inverse Operation on BOTH sides *Do the Math!!!! 3) Solution – Box –in 4) Check Answer Rewrite equation with Value substituted 5) Do Math and check BOTH sides

11. 2-Column Notes Example#3 18 + j =94 Step 1 -18 -18 Step 2 j = 76 Step 3 Check 18+76=94 Step 4 94 = 94 Step 5 Instructions – STEPS 1) Copy Problem 2) Inverse Operation on BOTH sides *Do the Math!!!! 3) Solution – Box –in 4) Check Answer Rewrite equation with Value substituted 5) Do Math and check BOTH sides

12. 2-Column Notes Example#4 Step 1 Step 2 Step 3 Step 4 Step 5 Instructions – STEPS 1) Copy Problem 2) Inverse Operation on BOTH sides *Do the Math!!!! 3) Solution – Box –in 4) Check Answer Rewrite equation with Value substituted 5) Do Math and check BOTH sides

13. 2-Column Notes Example#5 Step 1 Step 2 Step 3 Step 4 Step 5 Instructions – STEPS 1) Copy Problem 2) Inverse Operation on BOTH sides *Do the Math!!!! 3) Solution – Box –in 4) Check Answer Rewrite equation with Value substituted 5) Do Math and check BOTH sides

14. 2-Column Notes Example#6 Step 1 Step 2 Step 3 Step 4 Step 5 Instructions – STEPS 1) Copy Problem 2) Inverse Operation on BOTH sides *Do the Math!!!! 3) Solution – Box –in 4) Check Answer Rewrite equation with Value substituted 5) Do Math and check BOTH sides

15. When you solve equations that have one operation, you use an inverse operation to isolate the variable. You can also use inverse operations to solve equations that have more than one operation. n + 7 = 15 – 7 –7 n = 8 2x + 3 = 23 – 3 2x = 20You need to use another operation to isolate x. It is often a good plan to follow the order of operations in reverse when solving equations that have more than one operation. Course 2 12-1 Solving Two-Step Equations

16. Learn to solve two-step equations. Course 2 12-1 Solving Two-Step Equations

17. Write down the directions to get to Pope High School from Hightower Trail MS parking lot. Directions to the HS Explain how to return to Hightower Trail MS.

18. Can you think of any other situations where you have to work backwards??????

19. How can the order of operations help us solve equations???? List the order of operations 1. 2. 3. 4. Now list it going backwards 1. 2. 3. 4.

20. Solve. Check each answer. Additional Example 1A: Solving Two-Step Equations Using Division 9c + 3 = 39 – 3 –3 9c = 36 c = 4 Subtract 3 from both sides. Divide both sides by 9. 9c99c9 = 36 9 Course 2 12-1 Solving Two-Step Equations

21. Check. Additional Example 1A Continued 9c + 3 = 39 9(4) + 3 39 ?=?= ?=?= ?=?= 36 + 3 39 39 Substitute 4 for c. 4 is a solution. Course 2 12-1 Solving Two-Step Equations

22. Course 2 12-1 Solving Two-Step Equations Reverse the order of operations when solving equations that have more than one operation. Helpful Hint

23. Solve. Check the answer. 7c + 6 = 48 – 6 –6 7c = 42 c = 6 Subtract 6 from both sides. Divide both sides by 7. 7c77c7 = 42 7 Check It Out: Example 1A Course 2 12-1 Solving Two-Step Equations

24. Check It Out: Example 1A Continued Insert Lesson Title Here Check. 7c + 6 = 48 7(6) + 6 48 ?=?= ?=?= ?=?= 42 + 6 48 48 Substitute 6 for c. 6 is a solution. Course 2 12-1 Solving Two-Step Equations

25. Solve. Additional Example 2A: Solving Two-Step Equations Using Multiplication 6 + y5y5 = 21 y5y5 6 + – 6 –6 y5y5 = 15 y5y5 = (5)15(5) y = 75 Subtract 6 from both sides. Multiply both sides by 5. Course 2 12-1 Solving Two-Step Equations

26. Solve. Additional Example 2B: Solving Two-Step Equations Using Multiplication x7x7 – 11 = 9 x7x7 x7x7 = 20 x7x7 = (7)20 (7) x = 140 Add 11 to both sides. Multiply both sides by 7. +11 +11 Course 2 12-1 Solving Two-Step Equations

27. Check It Out: Example 2A Insert Lesson Title Here Solve. 8 + y2y2 = 48 y2y2 8 + – 8 –8 y2y2 = 40 y2y2 = (2)40 (2) y = 80 Subtract 8 from both sides. Multiply both sides by 2. Course 2 12-1 Solving Two-Step Equations

28. Check It Out: Example 2B Insert Lesson Title Here Solve. x5x5 – 31 = 19 x5x5 +31 +31 x5x5 = 50 x5x5 = (5)50 (5) x = 250 Add 31 to both sides. Multiply both sides by 5. Course 2 12-1 Solving Two-Step Equations

29. Out ticket Show each step and number each step Solve and Check 1. 4w – 3 = 25 2.