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3.3 Solve Multi-Step Equations Students will solve multi-step equations using Algebra. Students will do assigned homework. Students will study vocabulary words.

Daily Review For use after Lesson 12.1 Solve the equation = –14 a 4 ANSWER 80– 2. 6r – 12 = 6 ANSWER = 7y 2y + – ANSWER 4–

Solve an equation by combining like terms EXAMPLE 1 Solve 8x – 3x – 10 = 20. 8x – 3x – 10 = 20 Write original equation. If needed box the variables and circle the non-variables 5x – 10 = 20 Combine like terms. Boxes first and then circles 5x – = Add 10 to each side. 5x = 30 Simplify. Divide each side by 5. x = 6 Simplify. = x5x 5

EXAMPLE 2 Solve an equation using the distributive property Solve 7x + 2(x + 6) = 39.

EXAMPLE 2 METHOD 1 Show All Steps 7x + 2(x + 6) = 39 7x + 2x + 12 = 39 9x + 12 = 39 9x + 12 – 12 = 39 – 12 9x = 27 x = 3 = 9x9x Distribute first 2 x X and 2 x 6 Combine like terms (variables first) Solve the remaining 2-step equation

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.

GUIDED PRACTICE for Examples 1, 2, and 3 9d – 2d + 4 = Solve the equation. Check your solution. 4 ANSWER

EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 2w + 3(w + 4) = ANSWER Solve the equation. Check your solution.

EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 6x – 2(x – 5) = ANSWER Solve the equation. Check your solution.

Multiply by a reciprocal to solve an equation EXAMPLE 4 Write original equation. 3 2 (3x + 5) = – x = -24 Simplify by moving the 7.5 (use inverse operations). 4.5x = –31.5 Subtract 7.5 from each side. x = –7 Divide each side by (3x + 5) = –24 Solve. Distribute the 3/2 to the parentheses 3 2 (3x + 5) = –

Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example (z – 6) = Solve the equation. Check your solution. 22 ANSWER

Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example (3r + 4) = Solve the equation. Check your solution. 7 ANSWER

Multiply by a reciprocal to solve an equation EXAMPLE 4 GUIDED PRACTICE for Example (4a – 1) = 28 – Solve the equation. Check your solution. –8.5 ANSWER

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

EXAMPLE 5 SOLUTION Let x be the amount of time the cranes are not flying. Then 336 – x is the amount of time the cranes are flying. Write and solve an equation 2500 = 25 (336 – x)

EXAMPLE = 25(336 – x) Write equation = 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

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