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Chapter Chapter3 2 Solving Equations and Problem Solving Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 1 Section 3.4 Solving Linear Equations in One Variable and Problem Solving Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 2 Addition Subtraction Multiplication Division sum difference product quotient plus minus times divided added to subtracted from less than multiply shared equally among twice per increased by decrease by of divided by total twice/double/ triple divided into more than less Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 3 Example Write each phrase as an algebraic expression. Use x to represent “a number.” a. 8 increased by a number b. the quotient of a number and 7 c. the sum of 10 and twice a number Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 4 Writing Sentences as Equations Write each sentence as an equation. Use x to represent “a number.” a. 8 increased by a number is 12. b. Twice a number equals negative 12. c. The quotient of twice a number and 12 is equal to 15. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 5 Using Problem-Solving Steps to Solve Problems UNDERSTAND the problem. 2. CHOOSE a variable to represent the unknown. Use this variable to represent any other unknowns. TRANSLATE the problem into an equation. 3. SOLVE the equation. 4. STATE the results: Check the proposed solution in the stated problem and state your conclusion. 1. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 6 Example Twice a number plus 3 is the same as the number minus 6. Find the number. Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 7 Example The distance by road from Chicago to Los Angeles is 1091 miles more than the distance from Chicago to Boston. If the total of these two distances is 3017 miles, find the distance from Chicago to Boston. continued Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 8 Example A woman’s $57,000 estate is to be divided so that her husband receives twice as much as her son. How much will each receive? Copyright © 2015, 2011, 2008 Pearson Education, Inc. Slide 9