Download 12(k + 4) = 60 SOLUTION

2-5 Solve Multi-Step Equations
Solve each equation. Check your solution.
1. –12(k + 4) = 60
SOLUTION: Write the equation. Use the Distributive Property. Use the Addition Property of Equality and simplify. Use the
Division Property of Equality to isolate k. Then simplify the result.
To check the solution, replace k with –9 in the original equation.
The sentence is true. The solution is –9.
2. 8(3a + 6) = 9(2a – 4)
SOLUTION: Write the equation. Use the Distributive Property. Use the Subtraction Property of Equality to eliminate 18a from the
right side of the equation. Simplify. Now use the Subtraction Property of Equality to eliminate 48 from the left side of
the equation, and simplify. Then use the Division Property of Equality to isolate a. Simplify.
The solution is –14.
To check the solution, replace a with –14 in the original equation.
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sentence
is true.byThe
solution
3. is –14.
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2-5 Solve
Multi-Step
Equations
The sentence
is true.
The solution is –9.
2. 8(3a + 6) = 9(2a – 4)
SOLUTION: Write the equation. Use the Distributive Property. Use the Subtraction Property of Equality to eliminate 18a from the
right side of the equation. Simplify. Now use the Subtraction Property of Equality to eliminate 48 from the left side of
the equation, and simplify. Then use the Division Property of Equality to isolate a. Simplify.
The solution is –14.
To check the solution, replace a with –14 in the original equation.
The sentence is true. The solution is –14.
3. SOLUTION: Write the equation. Use the Distributive Property. Collect like terms. Use the Addition Property of Equality to
eliminate
h from the left side of the equation, and simplify. Use the Addition Property of Equality to eliminate 6
from the right side of the equation, and simplify. Then divide both sides by 3.
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The solution is 6.
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2-5 Solve
Multi-Step Equations
The sentence is true. The solution is –14.
3. SOLUTION: Write the equation. Use the Distributive Property. Collect like terms. Use the Addition Property of Equality to
eliminate
h from the left side of the equation, and simplify. Use the Addition Property of Equality to eliminate 6
from the right side of the equation, and simplify. Then divide both sides by 3.
The solution is 6.
To check the solution, replace h with 6 in the original equation.
The sentence is true. The solution is 6.
4. 8(c – 9) = 6(2c – 12) – 4c
SOLUTION: Write the equation. Use the Distributive Property and collect like terms. Then use the Properties of Equality to solve
the equation.
At this point, –72 always equals –72, so the equation is an identity. The solution is all real numbers.
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To check the solution, replace c with any number in the original equation. Let c = 0.
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2-5 Solve Multi-Step Equations
The sentence is true. The solution is 6.
4. 8(c – 9) = 6(2c – 12) – 4c
SOLUTION: Write the equation. Use the Distributive Property and collect like terms. Then use the Properties of Equality to solve
the equation.
At this point, –72 always equals –72, so the equation is an identity. The solution is all real numbers.
To check the solution, replace c with any number in the original equation. Let c = 0.
The sentence is true. Copy and Solve Solve each equation. Show your work on a separate piece of paper.
5. –10y + 18 = –3(5y – 7) + 5y
SOLUTION: Write the equation. Use the Distributive Property. Collect like terms. Then use the Properties of Equality to solve the
equation.
At this point, 18 never equals 21, so the solution is the null set or there is no solution. To check, replace y with any number. Let y = 1.
Eight does not equal 11, so there is no solution.
6. 8(t + 2) – 3(t – 4) = 6(t – 7) + 8
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SOLUTION: Write the equation. Use the Distributive Property, and collect like terms. Use the Subtraction Property of Equality,
and simplify. Use the Addition Property of Equality to isolate t. 2-5 Solve
Equations
Eight Multi-Step
does not equal
11, so there is no solution.
6. 8(t + 2) – 3(t – 4) = 6(t – 7) + 8
SOLUTION: Write the equation. Use the Distributive Property, and collect like terms. Use the Subtraction Property of Equality,
and simplify. Use the Addition Property of Equality to isolate t. The solution is 62.
To check the solution, replace t with 62 in the original equation.
The sentence is true. The solution is 62.
7. 4(5 + 2x) – 5 = 3(3x + 7)
SOLUTION: Write the equation. Use the Distributive Property, and collect like terms. Use the Subtraction Property of Equality, and simplify. Then use the Subtraction Property of Equality to isolate x. The solution is –6.
To check the solution, replace x with –6 in the original equation.
The sentence is true. The solution is –6.
8. 6(2x – 8) + 3 = 15
SOLUTION: eSolutions
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Write
the equation.
Use
the Distributive
Page 5
Property, and collect like terms. Use the Addition Property of Equality and
simplify. Use the Division Property of Equality to isolate x. Then simplify the result.
2-5 Solve Multi-Step Equations
The sentence is true. The solution is –6.
8. 6(2x – 8) + 3 = 15
SOLUTION: Write the equation. Use the Distributive Property, and collect like terms. Use the Addition Property of Equality and
simplify. Use the Division Property of Equality to isolate x. Then simplify the result.
To check the solution, replace x with 5 in the original equation.
The sentence is true. The solution is 5.
9. The school has budgeted $2,000 for an end-of-year party at the local park. The cost to rent the park shelter is $150.
How much can the student council spend per student on food if each of the 225 students receives a $3.50 gift?
SOLUTION: Words The school has $2,000 to spend. The cost is $150 plus the cost per guest. The cost for each of the 225 guests is $3.50 plus the cost of food.
Variable Let x represent the cost of each guest’s food.
Equation 2,000 = 150 + 225(3.5 + x)
Solve the equation for x. Use the Distributive Property, and collect like terms. Use the Subtraction Property of
Equality and simplify. Divide both sides by 225.
The student council can spend about $4.72 per person on food for the end-of-year party.
10. Reason Abstractly The table shows the number of students in each homeroom.
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2-5 Solve
Multi-Step Equations
The student council can spend about $4.72 per person on food for the end-of-year party.
10. Reason Abstractly The table shows the number of students in each homeroom.
a. Write an equation to find the number of students in Mr. Boggs’s homeroom if the total number of students is 90.
b. Solve the equation from part a to find the number of students in Mr. Boggs’s homeroom.
SOLUTION: a. The number of students in Mr. Boggs’s homeroom is equal to b. Add the total number of students in each class
and set it equal to 90.
90 = b + 1.5(b + 2) + 15 + (2b – 9)
Use the Distributive Property, and collect like terms.
90 = b + 1.5b + 3 + 15 + 2b – 9
90 = 4.5b + 9
b. Use the Subtraction Property of Equality, and simplify. Use the Division Property of Equality to isolate b. Simplify.
There are 18 students in Mr. Boggs’s homeroom.
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