Transcript 3CH2L8
2-8 Solving Two-Step Equations Warm Up Solve. 1. x + 12 = 35 x = 23 2. 8x = 120 x = 15 3. y = 7 y = 63 9 4. –34 = y + 56 y = –90 Course 3 2-8 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 the smallest possible x? (Hint: What is the smallest prime number?) x=3 Course 3 2-8 Solving Two-Step Equations TB P. 98-101 Learn to solve two-step equations. Course 3 2-8 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 2-8 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 2-8 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 Course 3 2-8 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 2-8 Solving Two-Step Equations Additional Example 1 Continued 3 Solve 650 = 443 + 45h –443 –443 207 = 207 = 45h 45 45 Subtract to undo the addition. 45h Divide to undo multiplication. 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong’s car. Course 3 2-8 Solving Two-Step Equations Additional Example 1 Continued 4 Look Back You can use a table to decide whether your answer is reasonable. Hours Labor 1 45 Parts $443 Total Cost $488 2 3 4 90 135 180 $443 $443 $443 $533 $578 $623 5 225 $443 $668 4.6 hours is a reasonable answer. Course 3 2-8 Solving Two-Step Equations 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 + 7 – 7 = 22 – 7 3 n 3 =3 3 n = 45 Course 3 15 Subtract 7 from both sides. Multiply both sides by 3. 2-8 Solving Two-Step Equations Additional Example 2A Continued Solve n + 7 = 22 3 Method 2: Multiply both sides of the equation by the denominator. (3) n + 7 = 22(3) 3 Multiply both sides by the denominator. n + 21 = 66 –21 n Course 3 –21 = 45 Subtract to undo addition. 2-8 Solving Two-Step Equations Additional Example 2B: Solving Two-Step Equations Solve y – 4 = 9 3 Method 1: Work backward to isolate the variable. y 4 Rewrite the expression as – =9 3 3 the sum of two fractions. 4 Think: First the variable is divided by 3, and then is 3 4 subtracted. To isolate the variable, add and then 3 multiply by 3. 4 y 4 4 4 Add to both sides. – + =9+ 3 3 3 3 3 31 y (3) = (3) Multiply both sides by 3. t3 3 y = 31 Course 3 2-8 Solving Two-Step Equations Additional Example 2B: Solving Two-Step Equations Solve y – 4 = 9 3 Method 2: Multiply both sides of the equation by the denominator. y – 4= 9 3 (3) y – 4 = 9(3) 3 Multiply both sides by the denominator. y – 4 = 27 +4 +4 y = 31 Course 3 Add to undo subtraction. 2-8 Solving Two-Step Equations Lesson Quiz Solve. 1. x – 3 = 10 –9 2. 7y + 25 = –24 x = –117 y = –7 3. –8.3 = –3.5x + 13.4 x = 6.2 4. y + 5 = 3 11 y = 28 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 Course 3