10 1 Solving TwoStep Equations Warm Up Problem

10 -1 Solving Two-Step Equations Warm Up Problem of the Day Lesson Presentation Course 3

10 -1 Solving Two-Step Equations Warm Up Solve. 1. x + 12 = 35 x = 23 2. 8 x = 120 x = 15 y 3. =7 9 y = 63 4. – 34 = y + 56 y = – 90 Course 3

10 -1 Solving Two-Step Equations Problem of the Day x is an odd integer. If you triple x and then subtract 7, you get a prime number. What is x? (Hint: Think about what the prime number must be in order for x to be an odd. ) x=3 Course 3

10 -1 Solving Two-Step Equations Learn to solve two-step equations. Course 3

10 -1 Solving Two-Step Equations Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “What is being done to the variable, and in what order? ” Then work backward to undo the operations. Course 3

10 -1 Solving Two-Step Equations Additional Example 1: Problem Solving Application The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 an hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car? Course 3

10 -1 Solving Two-Step Equations Additional Example 1 Continued 1 Understand the Problem List the important information: The answer is the number of hours the mechanic worked on the car. • The parts cost $443. • The labor cost $45 per hour. • The total bill was $650. Let h represent the hours the mechanic worked. Total bill = Parts + Labor 650 = 443 + 45 h Course 3

10 -1 Solving Two-Step Equations Additional Example 1 Continued 2 Make a Plan Think: First the variable is multiplied by 45, and then 443 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443 from both sides of the equation, and then divide both sides of the new equation by 45. Course 3

10 -1 Solving Two-Step Equations Additional Example 1 Continued 3 Solve 650 = 443 + 45 h – 443 207 = 45 h 45 45 Subtract to undo the addition. 45 h Divide to undo multiplication. 4. 6 = h The mechanic worked for 4. 6 hours on Mr. Wong’s car. Course 3

10 -1 Solving Two-Step Equations Additional Example 1 Continued 4 Look Back If the mechanic worked 4. 6 hours, the labor would be $45(4. 6) = $207. The sum of the parts and the labor would be $443 + $207 = $650. Course 3

10 -1 Solving Two-Step Equations Try This: Example 1 The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car? Course 3

10 -1 Solving Two-Step Equations Try This: Example 1 Continued 1 Understand the Problem List the important information: The answer is the number of hours the mechanic worked on your car. • The parts cost $275. • The labor cost $35 per hour. • The total bill was $850. Let h represent the hours the mechanic worked. Total bill = Parts + Labor 850 = 275 + 35 h Course 3

10 -1 Solving Two-Step Equations Try This: Example 1 Continued 2 Make a Plan Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35. Course 3

10 -1 Solving Two-Step Equations Try This: Example 1 Continued 3 Solve 850 = 275 + 35 h – 275 575 = 35 h 35 35 Subtract to undo the addition. 35 h Divide to undo multiplication. 16. 4 h The mechanic worked for about 16. 4 hours on your car. Course 3

10 -1 Solving Two-Step Equations Try This: Example 1 Continued 4 Look Back If the mechanic worked 16. 4 hours, the labor would be $35(16. 4) = $574. The sum of the parts and the labor would be $275 + $574 = $849. Course 3

10 -1 Solving Two-Step Equations Additional Example 2 A: Solving Two-Step Equations Solve. A. n + 7 = 22 3 Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3. n + 7 = 22 3 – 7 Subtract to undo addition. n = 15 3 n Multiply to undo division. 3 = 3 15 3 n = 45 Course 3

10 -1 Solving Two-Step Equations Additional Example 2 A Continued Check n + 7 = 22 3 ? 45 + 7 = 22 3 ? 15 + 7 = 22 Course 3 Substitute 45 into the original equation.

10 -1 Solving Two-Step Equations Additional Example 2 B: Solving Two-Step Equations B. 2. 7 = – 1. 3 m + 6. 6 Think: First the variable is multiplied by – 1. 3, and then 6. 6 is added. To isolate the variable, subtract 6. 6, and then divide by – 1. 3. 2. 7 = – 1. 3 m + 6. 6 – 3. 9 = – 1. 3 m – 1. 3 3=m Course 3 Subtract to undo addition. Divide to undo multiplication.

10 -1 Solving Two-Step Equations Additional Example 2 C: Solving Two-Step Equations C. y – 4 = 9 3 Think: First 4 is subtracted from the variable, and then the result is divided by 3. To isolate the variable, multiply by 3, and then add 4. y– 4 3 =9 y– 4 3 · 3 =3 · 9 y – 4 = 27 +4 +4 y = 31 Course 3 Multiply to undo division. Add to undo subtraction.

10 -1 Solving Two-Step Equations Try This: Example 2 A Solve. A. n + 5 = 29 4 Think: First the variable is divided by 4, and then 5 is added. To isolate the variable, subtract 5, and then multiply by 4. n + 5 = 29 4 – 5 4 n =4 4 n = 96 Course 3 Subtract to undo addition. 24 Multiply to undo division.

10 -1 Solving Two-Step Equations Try This: Example 2 A Continued Check n + 5 = 29 4 ? 96 + 5 = 29 4 ? 24 + 5 = 29 Course 3 Substitute 96 into the original equation.

10 -1 Solving Two-Step Equations Try This: Example 2 B B. 4. 8 = – 2. 3 m + 0. 2 Think: First the variable is multiplied by – 2. 3, and then 0. 2 is added. To isolate the variable, subtract 0. 2, and then divide by – 2. 3. 4. 8 = – 2. 3 m + 0. 2 – 0. 2 4. 6 = – 2. 3 m – 2. 3 – 2 = m Course 3 Subtract to undo addition. Divide to undo multiplication.

10 -1 Solving Two-Step Equations Try This: Example 2 C C. y – 2 = 8 4 Think: First 2 is subtracted from the variable, and then the result is divided by 4. To isolate the variable, multiply by 4, and then add 2. y– 2 4 =8 y– 2 4 · 4 =4 · 8 y – 2 = 32 +2 +2 y = 34 Course 3 Multiply to undo division. Add to undo subtraction.

10 -1 Solving Insert Lesson Two-Step Title Equations Here Solve. Lesson Quiz x – 3 = 10 x = – 117 – 9 2. 7 y + 25 = – 24 y = – 7 1. 3. – 8. 3 = – 3. 5 x + 13. 4 x = 6. 2 4. y + 5 = 3 y = 28 11 5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last? 24 months Course 3