3.3 Practice with Examples
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1 3.3 For use with pages NAME DATE GOAL Use two or more transformations to solve an equation and use multi-step equations to solve real-life problems EXAMPLE 1 Solving a Linear Equation Solve 3x 4 5. To isolate the variable x, undo the subtraction and then the multiplication. 3x 4 5 Write original equation. 3x Add 4 to each side. 3x 9 3x Divide each side by 3. x 3 The solution is 3. Check this in the original equation. Exercises for Example y m 1 3. x Algebra 1
2 3.3 NAME For use with pages DATE EXAMPLE 2 Using the Distributive Property and Combining Like Terms Solve y 5 y y 5 y 3 33 Write original equation. y 5y Use distributive property. 6y Combine like terms. 6y Subtract 15 from each side. 6y 18 6y Divide each side by y 3 The solution is 3. Check this in the original equation. Exercises for Example x 8 x b z Algebra 1 53
3 3.3 EXAMPLE 3 NAME For use with pages Solving a Real-Life Problem DATE The sum of the ages of two sisters is 25. The second sister s age is 5 more than three times the first sister s age n. Find the two ages. First sister s age n Second sister s age 3n 5 25 Solve n 3n n 3n 5 25 Write real-life equation. 4n 5 25 Combine like terms. 4n Subtract 5 from each side. 4n 20 4n Divide each side by n 5 The first sister s age is 5. The second sister s age is Exercises for Example 3 7. A parking garage charges $3 plus $1.50 per hour. You have $12 to spend for parking. Write and solve an equation to find the number of hours that you can park. 8. As a lifeguard, you earn $6 per day plus $2.50 per hour. Write and solve an equation to find how many hours you must work to earn $16 in one day. 54 Algebra 1
4 3.4 For use with pages NAME DATE GOAL Collect variables on one side of an equation and use equations to solve real-life problems VOCABULARY An identity is a linear equation that is true for all values of the variable. EXAMPLE 1 Collecting Variables on One Side Solve 20 3x 2x. Think of 20 3x as 20 3x. Since 2x is greater than 3x, collect the x-terms on the right side. 20 3x 2x Write original equation. 20 3x 3x 2x 3x Add 3x to each side. 20 5x x 5 4 x Exercises for Example q 7q 6 Divide each side by d 6 17d 3. y 7 8y Algebra 1 55
5 3.4 EXAMPLE 2 NAME DATE For use with pages Many Solutions or No Solution a. Solve 2x 3 2x 4. b. Solve t 5 t 5 a. 2x 3 2x 4 2x 3 3 2x 4 3 2x 2x Write original equation. Subtract 3 from each side. Subtract 2x from each side. The original equation has no solution, because 0 1 for any value of x. b. t 5 t 5 t 5 t Write original equation. Use distributive property. Add t to each side. All values of t are solutions, because 5 5is always true. The original equation is an identity. Exercises for Example z 3 9z 5. 2 f 7 2f n 3 5n 56 Algebra 1
6 3.4 EXAMPLE 3 NAME DATE For use with pages Solving Real-Life Problems A health club charges nonmembers $2 per day to swim and $5 per day for aerobics classes. Members pay a yearly fee of $200 plus $3 per day for aerobics classes. Write and solve an equation to find the number of days you must use the club to justify a yearly membership. Let n represent the number of days that you use the club. Then find the number of times for which the two plans would cost the same. 2n 5n 200 3n Write real-life equation. 7n 200 3n Combine like terms. 7n 3n 200 3n 3n Subtract 3n from each side. 4n 200 4n Divide each side by 4. n 50 You must use the club 50 days to justify a yearly membership. Exercises for Example 3 7. Rework Example 3 if nonmembers pay $3 per day to swim. 8. Rework Example 3 if members pay a yearly fee of $220. Algebra 1 57
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