Solving Two Step Equations 11-1 Notes 13 Solving Two Step Equations 11-1

When you solve equations that have one operation, you use an inverse operation to isolate the variable. n + 7 = 15 – 7 –7 n = 8 You can also use inverse operations to solve equations that have more than one operation. 2x + 3 = 23 You need to use another operation to isolate x. – 3 – 3 2x = 20

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 Check. 9c + 3 = 39 9(4) + 3 ? = 39 Substitute 4 for c. 36 + 3 39 ? = 39 39 ? = 4 is a solution.

Reverse the order of operations when solving equations that have more than one operation. Helpful Hint

Additional Example 1B: Solving Two-Step Equations Using Division Solve. Check the answer. –34 = –4m – 6 –34 = –4m – 6 + 6 +6 Add 6 to both sides. –28 = –4m –28 –4 = –4m Divide both sides by –4. 7 = m

Additional Example 1B Continued Check. –4m – 6 = –34 –4(7) – 6 ? = –34 Substitute 7 for m. –28 – 6 –34 ? = ? = –34 –34 7 is a solution.

Check It Out: Example 1A On your own. Solve. Check the answer. 7c + 6 = 48

Check It Out: Example 1B On your own. Solve. Check the answer. –6m – 8 = –50

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 Solve. x 7 – 11 = 9 x 7 – 11 = 9 +11 +11 Add 11 to both sides. x 7 = 20 x 7 (7)‏ = (7)20 Multiply both sides by 7. x = 140

Check It Out: Example 2A Solve. y 2 8 + = 48

Check It Out: Example 2B Solve. x 5 – 31 = 19

Additional Example 3: Consumer Math Application Jamie rented a canoe while she was on vacation. She paid a flat rental fee of $85.00, plus $7.50 each day. Her total cost was $130.00. For how many days did she rent the canoe? Let d represent the number of days she rented the canoe. 7.5d + 85 = 130 – 85 –85 Subtract 85 from both sides. 7.5d = 45 7.5d = 45 Divide both sides by 7.5. 7.5 7.5 d = 6 Jamie rented the canoe for 6 days.