Chapter 1Section 3

Write an algebraic expression to represent 3 more than a number.

Answer:

Write an algebraic expression to represent 6 times the cube of a number.

Answer:

Write an algebraic expression to represent the square of a number decreased by the product of 5 and the same number.

Answer:

Write an algebraic expression to represent twice the difference of a number and 6.

Answer:

Write an algebraic expression to represent each verbal expression.a. 6 more than a number

b. 2 less than the cube of a number

c. 10 decreased by the product of a number and 2

d. 3 times the difference of a number and 7

Answer:

Answer:

Answer:

Answer:

Write a verbal sentence to represent .

Answer: The sum of 14 and 9 is 23.

Write a verbal sentence to represent .

Answer: Six is equal to –5 plus a number.

Write a verbal sentence to represent .

Answer: Seven times a number minus 2 is 19.

Write a verbal sentence to represent each equation.a.

b.

c.

Answer: The difference between 10 and 3 is 7.

Answer: Three times a number plus 2 equals 11.

Answer: Five is equal to the sum of 2 and a number.

Name the property illustrated by the statement if xy = 28 and x = 7, then 7y = 28.

Answer: Substitution Property of Equality

Name the property illustrated by the statement.

Answer: Reflexive Property of Equality

Name the property illustrated by each statement.a.

b.

Answer: Transitive Property of Equality

Answer: Symmetric Property of Equality

Solve . Check your solution.

Original equation

Add 5.48 to each side.

Simplify.

Check: Original equation

Answer: The solution is 5.5.

Simplify.

Substitute 5.5 for s.

Solve . Check your solution.

Original equation

Simplify.

Multiply each side by the multiplicative inverse of

Answer: The solution is 36.

Check: Original equation

Simplify.

Substitute 36 for t.

Solve each equation. Check your solution.

a.

b.Answer: –2

Answer: 15

Solve

Original equation

Distributive and Substitution Properties

Commutative, Distributive, and Substitution Properties

Addition and Substitution Properties

Division and Substitution Properties

Answer: The solution is –19.

Answer: –6

Solve

Geometry The area of a trapezoid is

where A is the area, b1 is the length of one base, b2

is the length of the other base, and h is the height of

the trapezoid. Solve the formula for h.

Area of a trapezoid

Multiply each side by 2.

Simplify.

Divide each side by .

Simplify.

Answer:

Geometry The perimeter of a rectangle is where P is the perimeter, is the length, and w is the width of the rectangle. Solve the formula for w.

w

Answer:

Multiple-Choice Test Itemwhat is the value of

A B

C D

Read the Test ItemYou are asked to find the value of the expression 4g – 2. Your first thought might be to find the value of g and then evaluate the expression using this value. However, you are not required to find the value of g. Instead, you can use the Subtraction Property of Equality on the given equation to find the value of 4g – 2.

Solve the Test Item

Original equation

Subtract 7 from each side.

Answer: B

Multiple-Choice Test Itemwhat is the value of

A 12 B 6

C –6 D –12

Answer: D

Home Improvement Carl wants to replace the 5 windows in the 2nd-story bedrooms of his home. His neighbor Will is a carpenter and he has agreed to help install them for $250. If Carl has budgeted $1000 for the total cost, what is the maximum amount he can spend on each window?

Explore Let c represent the cost of each window.Plan

The number

of windowstime

s

the cost per

windowplus

the cost for a carpenter equals

the total cost.5 c + 250 = 1000

Solve Original equation

Subtract 250 from each side.Simplify.

Simplify.

Answer: Carl can afford to spend $150 on each window.

Divide each side by 5.

Examine The total cost to replace five windows at $150each is 5(150) or $750. Add the $250 cost ofthe carpenter to that, and the total bill toreplace the windows is 750 + 250 or $1000.Thus, the answer is correct.

Home Improvement Kelly wants to repair the siding on herhouse. Her contractor will charge her $300plus $150 per square foot of siding. How much siding can she repair for $1500?

Answer: 8 ft2