Solving Two-Step Equations Warm Up Problem of the Day Lesson Presentation 3
Warm Up Solve. 1. x + 12 = 35 2. 8x = 120 y 9 3. = 7 4. 34 = y + 56 x = 23 x = 15 y = 63 y = 90
Learn to solve 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 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?
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 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 3 Solve 650 = 443 + 45h 443 443 Subtract to undo the addition. 207 = 45h 207 45h 45 = 45 4.6 = h Divide to undo multiplication. The mechanic worked for 4.6 hours on Mr. Wong s car.
Check It Out: 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?
Check It Out: 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
Check It Out: 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.
Check It Out: Example 1 Continued 3 Solve 850 = 275 + 35h 275 275 Subtract to undo the addition. 575 = 35h 575 35h 35 = 35 16.4 h Divide to undo multiplication. The mechanic worked for about 16.4 hours on your car.
Additional Example 2A: Solving Two-Step Equations n Solve + 7 = 22 3 Method 1: Work backward to isolate the variable. 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 3 + 7 7 = 22 7 3 n = 3 15 3 n = 45 Subtract 7 from both sides. Multiply both sides by 3.
Additional Example 2A Continued Solve n + 7 = 22 3 Method 2: Multiply both sides of the equation by the denominator. (3) n 3 + 7 = 22(3) Multiply both sides by the denominator. n + 21 = 66 21 21 Subtract to undo addition. n = 45
Check It Out: Example 2A n Solve + 8 = 18 4 Method 1: Work backward to isolate the variable. Think: First the variable is divided by 4, and then 8 is added. To isolate the variable, subtract 8, and then multiply by 4. n 4 + 8 8 = 18 8 4 n = 4 10 4 n = 40 Subtract 8 from both sides. Multiply both sides by 4.
n Solve + 8 = 18 4 Check It Out: Example 2A Method 2: Multiply both sides of the equation by the denominator. (4) n 4 + 8 = 18(4) Multiply both sides by the denominator. n + 32 = 72 32 32 Subtract to undo addition. n = 40
Example using distributive property: Solve 2(x + 8) = 26
Solve. 1. x 3 = 10 9 2. 7y + 25 = 24 Lesson Quiz x = 117 y = 7 3. 8.3 = 3.5x + 13.4 4. 3(x+15) = 21 x = 6.2 X = 2 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 = 24