example 1-1a use the distributive property to write as an equivalent expression. then evaluate the...
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Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.
Answer: 52
Multiply.
Add.
Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.
Answer: 30
Multiply.
Add.
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression.
a.
b.
Answer:
Answer:
Recreation North Country Rivers of York, Maine, offers one-day white-water rafting trips on the Kennebec River. The trip costs $69 per person, and wet suits are $15 each.
Write two equivalent expressions to find the total cost of one trip for a family of four if each person uses a wet suit.
Method 1 Find the cost for 1 person, then multiply by 4.
cost for 1 person
Method 2 Find the cost of 4 trips and 4 wet suits. Then add.
cost of 4 wet suitscost of 4 trips
Evaluate either expression to find the total cost.
Distributive Property
Multiply.
Add.
Answer: The total cost is $336.
Check You can check your results by evaluating 4($84).
Movies The cost of a movie ticket is $7 and the cost of a box of popcorn is $2.
a. Write two equivalent expressions to find the total cost for a family of five to go to the movies if each member of the family gets a box of popcorn.
b. Find the total cost.
Answer: $45
Answer:
Use the Distributive Property to write as an equivalent algebraic expression.
Simplify.
Answer:
Use the Distributive Property to write as an equivalent algebraic expression.
Simplify.
Answer:
Use the Distributive Property to write each expression as an equivalent algebraic expression.
a.
b.
Answer:
Answer:
Use the Distributive Property to write as an equivalent algebraic expression.
Rewrite as
Distributive Property
Simplify.
Definition of subtraction
Answer:
Use the Distributive Property to write as an equivalent algebraic expression.
Distributive Property
Simplify.
Answer:
Rewrite as
Use the Distributive Property to write each expression as an equivalent algebraic expression.
a.
b.
Answer:
Answer:
Example 1 Identify Parts of Expressions
Example 2 Simplify Algebraic Expressions
Example 3 Translate Verbal Phrases into Expressions
Definition ofsubtraction
Identity Property
Answer: The terms are 4x, –x, 2y, and –3. The like terms are 4x and –x. The coefficients are 4, –1, and 2. The constant is –3.
Identify the terms, like terms, coefficients, and constants in the expression
Answer: The terms are 5x, 3y, –2y, and 6. The like terms are 3y and –2y. The coefficients are 5, 3, and –2. The constant is 6.
Identify the terms, like terms, coefficients, and constants in the expression
Simplify .
5x and 4x are like terms.
Simplify.
Answer: 9x
Distributive Property
Simplify .
8n and 4n are like terms.
Distributive Property
Simplify.
Answer:
Commutative Property
Simplify .
6x and –5x are like terms. 4 and –7 are also like terms.
Commutative Property
Distributive Property
Definition of subtraction
Answer:
Simplify.
Simplify .
Multiply.
Identity Property
Distributive Property
Commutative Property
Answer:
Distributive Property
Simplify.
Answer:
Simplify each expression.
a.
b.
c.
d.
Answer:
Answer:
Answer:
Work You and a friend worked in the school store last week. You worked 4 hours more than your friend. Write an expression in simplest form that represents the total number of hours you both worked.
Words Your friend worked some hours. You worked 4 more hours than your friend.
Variables Let number of hours your friend worked.Let number of hours you worked.
Expression To find the total, add the expressions.
Associative Property
Identity Property
Distributive Property
Simplify.
Answer: The expression represents the total number of hours worked, where h is the number of hours your friend worked.
Library Books You and a friend went to the library. Your friend borrowed three more books than you did. Write an expression in simplest form that represents the total number of books you both borrowed.
Answer:
Example 1 Solve Equations by Subtracting
Example 2 Graph the Solutions of an Equation
Example 3 Solve Equations by Adding
Example 4 Use an Equation to Solve a Problem
Example 5 Solve Equations
Solve . Check your solution.
Write the equation.
Subtract 4 from each side.
Identity Property;
To check your solution, replace x with –7 in the original equation.
Check Write the equation.
The sentence is true.
Answer: The solution is –7.
Check to see whether this sentence is true.
Solve . Check your solution.
Answer: –4
Graph the solution of on a number line.
Answer: The solution is –1. To graph the solution, draw a dot at –1 on a number line.
Write the equation.
Subtract 8 from each side.
Simplify.
Graph the solution of on a number line.
Answer:
Solve .
Write the equation.
Add 3 to each side.
Additive Inverse Property;
Identity Property;
Rewrite as
Answer: The solution is –11. Check your solution.
Solve .
Answer: –7
Entertainment Movie A earned $225 million at the box office. That is $38 million less than Movie B earned. Write and solve an equation to find the amount Movie B earned.
Words Movie A earned $38 million less than Movie B earned.
Variables Let amount Movie B earned.
Movie A earned $38 million less than Movie B.
Equation 225
Solve the equation.
Think of as
Add 38 to each side.
Simplify.
Answer: Movie B earned $263 million at the box office.
Construction Board A measures 22 feet. That is 9 feet more than the measure of board B. Write and solve an equation to find the measure of board B.
Answer:
Read the Test Item To find the value of x, solve the equation.
Multiple-Choice Test Item
What value of x makes a true statement.
A 9 B 7 C –7 D –9
Solve the Test Item
Write the equation.
Add 1 to each side.
Simplify.
Answer: A
Multiple-Choice Test Item
What value of x makes a true statement?
A 2 B –2 C –8 D 1
Answer: B
Example 1 Solve Equations by Dividing
Example 2 Use an Equation to Solve a Problem
Example 3 Solve Equations by Multiplying
Solve . Check your solution and graph it on a number line.
Write the equation.
Divide each side by 7.
,
Identity Property;
To check your solution, replace x with –8 in the original equation.
The statement is true.
Answer: The solution is –8.
Check Write the equation.
Check to see whether this statement is true.
To graph the solution, draw a dot at –8 on a number line.
Solve . Check your solution and graph it on a number line.
Answer: The solution is –3.
Hobbies Esteban spent $112 on boxes of baseball cards. If he paid $14 per box, how many boxes of cards did Esteban buy?
Words $14 times the number of boxes equals the total.
Variables Let x represent the number of boxes.
the number of boxes
The cost per box times equals the total.
Equation $14 x $112•
Solve the equation.
Write the equation.
Divide each side by 14.
Simplify.
The statement is true.
Answer: Therefore, Estaban bought 8 boxes of cards.
Check Write the equation.
Check to see whether this statement is true.
Toy Cars Drew spent $18 on toy cars. If the cars cost $2 each, how many cars did Drew buy?
Answer: Drew bought 9 cars.
Solve . Check your solution.
Write the equation.
Multiply each side by –5 to undo the division.
Simplify.
The statement is true.
Answer: The solution is 60.
Check to see whether this statement is true.
Check Write the equation.
Solve . Check your solution.
Answer: –36
Example 1 Solve Two-Step Equations
Example 2 Use an Equation to Solve a Problem
Example 3 Equations with Negative Coefficients
Example 4 Combine Like Terms Before Solving
Solve . Check your solution.
Write the equation.
Undo subtraction. Add 4 to each side.
Simplify.
Undo multiplication. Divide each side by 3.
Simplify.
The statement is true.
Answer: The solution is 7.
Check Write the equation.
Check to see whether this statement is true.
Solve .
Write the equation.
Undo addition. Subtract 8 from each side.
Simplify.
Undo division. Multiply each side by 5.
Simplify.
Answer: The solution is –25. Check your solution.
Answer: 4
Answer: 24
a. Solve .Check your solution.
b. Solve .
Measurement The formula can be used to convert Fahrenheit degrees to Celsius degrees. Solve the equation to find the equivalent Celsius temperature for 59°F.
Write the equation.
Subtract 32 from each side.
Simplify.
Divide each side by 1.8.
Simplify.
Answer: The solution is 15.
Therefore, 15° Celsius is the equivalent temperature to 59° Fahrenheit.
Cell Phones Sue signed up for a cell phone plan that charges $19 per month plus $0.10 per minute used. Her first bill was $23.30. Solve to find out how many minutes Sue used this month.
Answer: 43 minutes
Solve .
Definition of subtraction
Add –5 to each side.
Simplify.
Write the equation.
Identity Property;
Divide each side by –1.
Simplify.
Check your solution.Answer: The solution is –2.
Solve .
Answer: –13
Solve .
Write the equation.
Identity Property;
Combine like terms, 1b and –3b.
Subtract 8 from each side.
Simplify.
Divide each side by –2.
Simplify.
Answer: The solution is –5.
Answer: –1
Solve .
Example 1 Translate Sentences into Equations
Example 2 Translate and Solve an Equation
Example 3 Write and Solve a Two-Step Equation
Example 4 Write and Solve a Two-Step Equation
Translate this sentence into an equation.
Twice a number increased by 5 equals –25.
Answer: The equation is .
Translate this sentence into an equation.
Four times a number minus 8 equals 28.
Answer: The equation is .
Answer: The equation is .
Translate this sentence into an equation.
When five is added to the product of a number and 8, the result is 12.
Translate each sentence into an equation.
a. Five times a number decreased by 9 equals –6.
b. Three times a number increased by 7 equals 18.
c. When seven is subtracted from the product of 2and a number, the result is 10.
Answer:
Answer:
Answer:
Nine more than four times a number is 41. Find the number.
Words Nine more than four times a number is 41.
Variable Let the number.
Subtract 9 from each side.
Simplify.
Mentally divide each side by 4.
Answer: Therefore, the number is 8.
Write the equation.Equation
Six less than three times a number is 15. Find the number.
Answer: 7
Variable Let her daughter’s earnings.
Earnings Ms. Blake earns $48,400 per year. This is $4150 more than three times as much as her daughter earns. How much does her daughter earn?
Words Ms. Blake earns $4150 more than three times as much as her daughter.
Ms. Blake $4150morethanearns
three times as much as her
daughter
Equation $48,400 3d$4150
Write the equation.
Subtract 4150 from each side.
Simplify.
Divide each side by 3.
Simplify.
Answer: Ms. Blake’s daughter earns $14,750.
Shopping Tami spent $175 at the grocery store. That is $25 less than four times as much as Ted spent. How much did Ted spend?
Answer: Ted spent $50.
Community Service In a canned food drive, Sam collected 12 more cans than Louise. Together, they collected 128 cans. How many cans did Sam collect?
Words Together, they collected 128 cans.
Variables Let number of cans collected by Louise.Then number of cans collected by Sam.Equation Write the equation.
Associative Property
Combine like terms.
Subtract 12 from each side.
Simplify.
Answer: So, Louise collected 58 cans and Sam collectedor 70 cans.
Mentally divide each side by 2.
Gardening During the summer, Kyle picked eight more tomatoes from his garden than Matt picked from his garden. Together, they picked 32 tomatoes. How many tomatoes did Kyle pick?
Answer: Kyle picked 20 tomatoes.
Example 1 Use the Distance Formula
Example 2 Find the Perimeter of a Rectangle
Example 3 Find a Missing Length
Example 4 Find the Area of a Rectangle
Example 5 Find a Missing Width
Travel If you travel 135 miles in 3 hours, what is your average speed in miles per hour?
Write the formula.
Replace d with 135 and t with 3.
Divide each side by 3.
Simplify.
Answer: The average speed is 45 miles per hour.
Vacation If you drive 520 miles in 8 hours to reach your vacation destination, what is your average speed in miles per hour?
Answer: Your average speed is 65 miles per hour.
Find the perimeter of the rectangle.
15 cm
20 cm
Write the formula.
Replace with 20 and w with 15.
Add 20 and 15.
Simplify.
Answer: The perimeter is 70 centimeters.
Find the perimeter of the rectangle.
Answer: The perimeter is 40 inches.
14 in.
6 in.
The perimeter of a rectangle is 60 feet. Its width is 9 feet. Find its length.
Write the formula.
Distributive Property
Replace P with 60 and w with 9.
Simplify.
Subtract 18 from each side.
Simplify.
Mentally divide each side by 2.
Answer: The length is 21 feet.
The perimeter of a rectangle is 36 meters. Its width is 6 meters. Find its length.
Answer: The length is 12 meters.
Find the area of a rectangle with length 14 feet and width 6 feet.
Write the formula.
Simplify.
Replace with 14 and w with 6.
Answer: The area is 84 square feet.
Find the area of a rectangle with length 11 yards and width 6 yards.
Answer: The area is 66 square yards.
The area of a rectangle is 40 square meters. Its length is 8 meters. Find its width.
Mentally divide each side by 8.
Replace A with 40 and with 8.
Answer: The width is 5 meters.
Write the formula.
The area of a rectangle is 42 square inches. Its length is 14 inches. Find its width.
Answer: The width is 3 inches.