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

Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Warm Up Solve. 1. x + 12 = 35 2. 8x = 120 3. = 7 4. –34 = y + 56 x = 23 x = 15 y9 y = 63 y = –90

Solving Two-Step Equations 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

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

Solving 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.

Additional Example 1: Problem Solving Application 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?

Understand the Problem 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 + 45h

Additional Example 1 Continued 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.

Additional Example 1 Continued Course 3 10-1 Solving Two-Step Equations Additional Example 1 Continued Solve 3 650 = 443 + 45h –443 –443 Subtract to undo the addition. 207 = 45h 207 45h 45 45 = Divide to undo multiplication. 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong’s car.

Additional Example 1 Continued Course 3 10-1 Solving Two-Step Equations Additional Example 1 Continued Look Back 4 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.

Solving Two-Step Equations 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?

Understand the Problem 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 + 35h

Try This: Example 1 Continued 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.

Try This: Example 1 Continued Course 3 10-1 Solving Two-Step Equations Try This: Example 1 Continued Solve 3 850 = 275 + 35h –275 –275 Subtract to undo the addition. 575 = 35h 575 35h 35 35 = Divide to undo multiplication. 16.4  h The mechanic worked for about 16.4 hours on your car.

Try This: Example 1 Continued Course 3 10-1 Solving Two-Step Equations Try This: Example 1 Continued Look Back 4 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.

Additional Example 2A: Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Additional Example 2A: Solving Two-Step Equations Solve. n3 A. + 7 = 22 Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3. + 7 = 22 n3 – 7 – 7 Subtract to undo addition. n3 = 15 Multiply to undo division. 3  = 3  15 n3 n = 45

Additional Example 2A Continued Course 3 10-1 Solving Two-Step Equations Additional Example 2A Continued + 7 = 22 n3 Check ? + 7 = 22 45 3 Substitute 45 into the original equation. 15 + 7 = 22 ? 

Additional Example 2B: Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Additional Example 2B: Solving Two-Step Equations B. 2.7 = –1.3m + 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 = –1.3m + 6.6 –6.6 –6.6 Subtract to undo addition. –3.9 = –1.3m –1.3 –1.3 –3.9 = –1.3m Divide to undo multiplication. 3 = m

Additional Example 2C: Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Additional Example 2C: Solving Two-Step Equations C. = 9 y – 4 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. = 9 y – 4 3 3 · 3 · Multiply to undo division. = 9 y – 4 3 y – 4 = 27 + 4 + 4 Add to undo subtraction. y = 31

Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Try This: Example 2A Solve. n4 A. + 5 = 29 Think: First the variable is divided by 4, and then 5 is added. To isolate the variable, subtract 5, and then multiply by 4. + 5 = 29 n4 – 5 – 5 Subtract to undo addition. Multiply to undo division. 4  = 4  24 n4 n = 96

Try This: Example 2A Continued Course 3 10-1 Solving Two-Step Equations Try This: Example 2A Continued + 5 = 29 n4 Check ? + 5 = 29 96 4 Substitute 96 into the original equation. 24 + 5 = 29 ? 

Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Try This: Example 2B B. 4.8 = –2.3m + 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 = –2.3m + 0.2 –0.2 –0.2 Subtract to undo addition. 4.6 = –2.3m –2.3 –2.3 4.6 = –2.3m Divide to undo multiplication. –2 = m

Solving Two-Step Equations Course 3 10-1 Solving Two-Step Equations Try This: Example 2C C. = 8 y – 2 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. = 8 y – 2 4 4 · 4 · Multiply to undo division. = 8 y – 2 4 y – 2 = 32 + 2 + 2 Add to undo subtraction. y = 34

Solving Two-Step Equations Insert Lesson Title Here Course 3 10-1 Solving Two-Step Equations Insert Lesson Title Here Lesson Quiz Solve. 1. – 3 = 10 2. 7y + 25 = –24 3. –8.3 = –3.5x + 13.4 4. = 3 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? x –9 x = –117 y = –7 x = 6.2 y + 5 11 y = 28 24 months