Equations - Introduction Must show ALL steps and ALL work for credit

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

Equations and Their Solutions Course 2 1-10 Equations and Their Solutions 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. Number of CDs Ella has 22 is equal to = 9 more than Kay has j + 9 Left expression Right expression

Equations and Their Solutions Course 2 1-10 Equations and Their Solutions 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. Reading Math The symbol ≠ means “is not equal to.”

 Equations and Their Solutions 1-10 Course 2 1-10 Equations and Their Solutions Additional Example 1A: 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. 26 t + 9 = 17 26 + 9 = 17 ? Substitute 26 for t. 35 = 17 ?  26 is not a solution of t + 9 = 17.

 Equations and Their Solutions 1-10 Course 2 1-10 Equations and Their Solutions 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 t + 9 = 17 8 + 9 = 17 ? Substitute 8 for t. 17 = 17 ?  8 is a solution of t + 9 = 17.

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

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!!!

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

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

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

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

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

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

Try on your own 1. r + 6 = -3 3. h/-3 = 12 2. -1 = q – 8 4. 63 = -9d

Solving Two-Step Equations Course 2 12-1 Solving Two-Step Equations 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. 2x + 3 = 23 n + 7 = 15 – 7 –7 – 3 – 3 n = 8 2x = 20 You 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.

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

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.

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

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.

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

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

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

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

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

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

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

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

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

Out ticket Show each step and number each step Solve and Check 2.