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3-2 HW: Pg. 144-146 #4-34e, 38, 40, 46-47

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46.) B 47.) C

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Solve an equation by combining like terms EXAMPLE 1 Solve 8x – 3x – 10 = 20. 5x – 10 = 20 Combine like terms. + 10 + 10 Add 10 to each side. 5x = 30 Simplify. Divide each side by 5. x = 6 Simplify. 55

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EXAMPLE 2 Solve an equation using the distributive property Solve 7x + 2(x + 6) = 39. SOLUTION Show All Steps 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 9x + 12 = 39 – 12 – 12 x = 3 = 9x9x 9 27 9

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Standardized Test Practice EXAMPLE 3 ANSWER The correct answer is D. A CD B SOLUTION In Step 2, the distributive property is used to simplify the left side of the equation. Because –4(x – 3) = –4x + 12, Step 2 should be 5x – 4x + 12 = 17.

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GUIDED PRACTICE for Examples 1, 2, and 3 9d – 2d + 4 = 32 1. Solve the equation. Check your solution. 4 ANSWER 2w + 3(w + 4) = 27 2. 3 ANSWER 6x – 2(x – 5) = 46 3. 9 ANSWER

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Multiply by a reciprocal to solve an equation EXAMPLE 4 2 3 3 2 (3x + 5) = (–24) 2 3 Multiply each side by, the reciprocal of. 2 3 3 2 3x + 5 = –16 Simplify. 3x = –21 Subtract 5 from each side. x = –7 Divide each side by 3. 3 2 (3x + 5) = –24 Solve. -5 -5 3 3

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Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example 4 3 4 (z – 6) = 12 4. Solve the equation. Check your solution. 22 ANSWER 6. 4 5 (4a – 1) = 28 – –8.5 ANSWER 2 5 (3r + 4) = 10 5. 7 ANSWER

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Write and solve an equation EXAMPLE 5 A flock of cranes migrates from Canada to Texas. The cranes take 14 days ( 336 hours) to travel 2500 miles. The cranes fly at an average speed of 25 miles per hour. How many hours of the migration are the cranes not flying? BIRD MIGRATION SOLUTION Let x be the amount of time the cranes are not flying. Then 336 – x is the amount of time they are flying. 2500 = 25 (336 – x)

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EXAMPLE 5 2500 = 25(336 – x) Write equation. 2500 = 8400 – 25x Distributive property –5900 = –25x Subtract 8400 from each side. 236 = x Divide each side by –25. ANSWER The cranes were not flying for 236 hours of the migration. Write and solve an equation -8400 -25 -25

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EXAMPLE 5 Write and solve an equation GUIDED PRACTICE for Example 5 7. WHAT IF? Suppose the cranes take 12 days ( 288 hours) to travel the 2500 miles. How many hours of this migration are the cranes not flying? 188 h ANSWER

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Summary How do you solve multi-step equations? ANS: Simplify 1 or both sides, then use inverse operations to get variable by itself. How do you deal with a problem that has a fraction being distributed to 2 terms on one side? ANS: multiply by the reciprocal on both sides first. What is wrong with this problem:

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Check Yourself Pg. 150-153 #4-16eoe,18-28e,38, 44-45 & Quiz 1 Pg. 153 #1-13 to prepare for Chapter 3 Quiz 1 next class

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