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Multi Step Equations
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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.
1. + 6 = –14 a 4
ANSWER 80–
2. 6r – 12 = 6
ANSWER 3
3. 36 = 7y 2y+–
ANSWER 4–
Solve an equation by combining like termsEXAMPLE 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 – 10 + 10 = 20 + 10 Add 10 to each side.
5x = 30 Simplify.
Divide each side by 5.
x = 6 Simplify.
= 305
5x5
EXAMPLE 2 Solve an equation using the distributive property
Solve 7x + 2(x + 6) = 39.
EXAMPLE 2
METHOD 1Show All Steps
7x + 2(x + 6) = 39
7x + 2x + 12 = 39
9x + 12 = 39
9x + 12 – 12 = 39 – 12
9x = 27
x = 3=
9x9
279
Distribute first 2 x X and 2 x 6
Combine like terms (variables first)
Solve the remaining 2-step equation
Standardized Test PracticeEXAMPLE 3
ANSWER
The correct answer is D. A C DB
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 = 321.
Solve the equation. Check your solution.
4ANSWER
EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3
2w + 3(w + 4) = 272.
3ANSWER
Solve the equation. Check your solution.
EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3
6x – 2(x – 5) = 463.
9ANSWER
Solve the equation. Check your solution.
Multiply by a reciprocal to solve an equation
EXAMPLE 4
Write original equation.32
(3x + 5) = –24
4.5 x + 7.5 = -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 4.5.
32
(3x + 5) = –24Solve .
Distribute the 3/2 to the parentheses32
(3x + 5) = –24
- 7.5 -7.5
4.5 4.5
Multiply by a reciprocal to solve an equation
EXAMPLE 4GUIDED PRACTICE for Example 4
34
(z – 6) = 124.
Solve the equation. Check your solution.
22ANSWER
Multiply by a reciprocal to solve an equation
EXAMPLE 4GUIDED PRACTICE for Example 4
25
(3r + 4) = 105.
Solve the equation. Check your solution.
7ANSWER
Multiply by a reciprocal to solve an equationEXAMPLE 4GUIDED PRACTICE for Example 4
6. 45
(4a – 1) = 28–
Solve the equation. Check your solution.
–8.5ANSWER
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 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
EXAMPLE 5 Write and solve an equationGUIDED 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 hANSWER