. Solving Multi-Step Equations How can you solve a multi-step equation? How can you check the reasonableness of your solution? ACTIVITY: Solving for the Angles of a Triangle Work with a partner. Write an equation for each triangle. Solve the equation to find the value of the variable. Then find the angle measures of each triangle. Use a protractor to check the reasonableness of your answer. a. b. (x + 0) 4 (x + 5) c. q q d. m q (m + 0) m COMMON CORE Solving Equations In this lesson, you will write and solve multi-step equations. solve real-life problems. e. y (y 0) f. Learning Standards A.CED. A.REI. A.REI. (t + 0.5) t 0 Chapter Solving Linear Equations
ACTIVITY: Problem-Solving Strategy Math Practice Consider Similar Problems What do you know about triangles? How can you use the methods from the previous activity to help you find angle measures? Work with a partner. The six triangles form a rectangle. Find the angle measures of each triangle. Use a protractor to check the reasonableness of your answers. t p p f w y m (t + 5) k p s m ACTIVITY: Puzzle Work with a partner. A survey asked 00 people to name their favorite weekday. The results are shown in the circle graph. a. How many degrees are in each part of the circle graph? b. What percent of the people chose each day? c. How many people chose each day? d. Organize your results in a table. Monday Favorite Weekday Tuesday Wednesday Friday Thursday 4. IN YOUR OWN WORDS How can you solve a multi-step equation? How can you check the reasonableness of your solution? Use what you learned about solving multi-step equations to complete Exercises 5 on page 4. Section. Solving Multi-Step Equations
. Lesson Lesson Tutorials Solving Multi-Step Equations To solve multi-step equations, use inverse operations to isolate the variable. Solving a Two-Step Equation The height (in feet) of a tree after x years is.5x + 5. After how many years is the tree 4 feet tall?.5x + 5 = 4 Write an equation. Undo the addition. Undo the multiplication. 5 5.5x = 9.5x.5 = 9.5 x = 6 Subtract 5 from each side. Divide each side by.5. The tree is 4 feet tall after 6 years. Combining Like Terms to Solve an Equation Solve 8x 6x 5 = 5. Undo the subtraction. Undo the multiplication. 8x 6x 5 = 5 x 5 = 5 Write the equation. Combine like terms. + 5 + 5 Add 5 to each side. x = 0 x = 0 x = 5 The solution is x = 5. Divide each side by. Exercises 6 9 Solve the equation. Check your solution.. z + = 7. x 9 = 5. 4n 8n + 7 = Chapter Solving Linear Equations
Study Tip Here is another way to solve the equation in Example. ( 5x) + 4 = 8 ( 5x) = 5x = 6 5x = 7 x =.4 Using the Distributive Property to Solve an Equation Solve ( 5x) + 4 = 8. ( 5x) + 4 = 8 Write the equation. () (5x) + 4 = 8 Use Distributive Property. 0x + 4 = 8 Multiply. 0x + 6 = 8 Combine like terms. 6 6 Subtract 6 from each side. 0x = 4 0x 0 = 4 0 x =.4 Divide each side by 0. 4 Real-Life Application sum of the data number of values Undo the division. Undo the addition. Use the table to find the number of miles x you need to run on Friday so that the mean number of miles run per day is.5. Write an equation using the definition of mean. + 0 +.5 + 0 + x =.5 Write the equation. 5.5 + x =.5 Combine like terms. 5 5.5 + x = 5 5.5 Multiply each side by 5..5 + x = 7.5.5.5 Subtract.5 from each side. x = 4 You need to run 4 miles on Friday. Day Miles Monday Tuesday 0 Wednesday.5 Thursday 0 Friday x Exercises 0 and Solve the equation. Check your solution. 4. (x + ) + 5x = 9 5. 5 +.5(d ) = 0.5 6. You scored 88, 9, and 87 on three tests. Write and solve an equation to find the score you need on the fourth test so that your mean test score is 90. Section. Solving Multi-Step Equations
. Exercises Help with Homework. WRITING Write the verbal statement as an equation. Then solve. more than times a number is 7.. OPEN-ENDED Explain how to solve the equation (4x ) + 9 = 9. 9+(-6)= +(-)= 4+(-9)= 9+(-)= CHOOSE TOOLS Find the value of the variable. Then find the angle measures of the polygon. Check the reasonableness of your answer.. k 4. a 5. b 45 k Sum of angle measures: 80 a a a (b + 45) b (b 90) 90 Solve the equation. Check your solution. Sum of angle measures: 60 6. 0x + = 7. 9 4c = 7 8..x +.x 5.4 = 0 9. h h + = 8 Sum of angle measures: 540 0. 6(5 8v) + = 54. ( x) + x = 44. ERROR ANALYSIS Describe and correct the error in solving the equation. (7 y) + 4 = 4 4 y + 4 = 4 0 y = 4 y = 6 y = 6 x. WATCHES The cost C (in dollars) of making n watches is represented by C = 5n + 85. How many watches are made when the cost is $85? x 4. HOUSE The height of the house is 6 feet. What is the height x of each story? 4 Chapter Solving Linear Equations
In Exercises 5 7, write and solve an equation to answer the question. 5. POSTCARD The area of the postcard is 4 square inches. What is the width b of the message (in inches)? 6. BREAKFAST You order two servings of pancakes and a fruit cup. The cost of the fruit cup is $.50. You leave a 5% tip. Your total bill is $.50. How much does one serving of pancakes cost? 4 in. Attendance 400 500 800 00 400 700 Theater Attendance 90 580 x 7. PROBLEM SOLVING How many people must attend the third show so that the average attendance for the three shows is 000? b in. 0 Show The letters a, b, and c represent constants. Solve the equation for x. 8. x + a = 4 9. bx = 7 0. bx bx = 8. 4cx b = 5b. ax b =.5. ax + b = c 4. DIVING Divers in a competition are scored by an international panel of judges. The highest and lowest scores are dropped. The total of the remaining scores is multiplied by the degree of difficulty of the dive. This product is multiplied by 0.6 to determine the final score. a. A diver s final score is 77.7. What is the degree of difficulty of the dive? Judge Russia China Mexico Germany Italy Japan Brazil Score 7.5 8.0 6.5 8.5 7.0 7.5 7.0 b. The degree of difficulty of a dive is 4.0. The diver s final score is 97.. Judges award half or whole points from 0 to 0. What scores could the judges have given the diver? Let a = and b =. Copy and complete the statement using <, >, or =. (Skills Review Handbook) 5. 5a 4 6. 5 b + 7 7. a 4 0b + 8 8. MULTIPLE CHOICE What value of x makes the equation x + 5 = x true? (Skills Review Handbook) A B 0 C D 5 Section. Solving Multi-Step Equations 5