Homework 1
Name: _____________________________________________ Chapter 7 Page 218 - 255
Practice 7.1 - Writing Algebraic Expressions
Write an algebraic expressions for each of the following.
1) The sum of 4 and p
2) The difference “8 less than q”
3) The product of 3 and r
4) The quotient of s and 5
5) Cheryl is now c years old.
a) Her father is 24 years older than Cheryl. Find her father’s age in terms of c.
b) Her brother is 2 years younger than Cheryl. Find her brother’s age in terms of c.
c) Her sister is twice as old as Cheryl. Find her sister’s age in terms of c.
d) Her cousin is
1
Cheryl’s age. Find her cousins age in terms of c.
3
Homework 2
Write an algebraic expressions for each of the following.
6) Multiply k by 5, and then add 3 to the product. ___________________________
7) Divide m by 7, and then subtract 4 from the quotient. ________________________
8) Divide j by 9, and then multiply the quotient by 2. ___________________________
9) The sum of
1
1
of z and of z. ___________________________
3
5
Solve.
10) Jeremy bought 5 pencils for d dollars. Each pen costs 35ȼ more than a pencil.
a) Write an algebraic expression for the cost, in dollars, of a pen.
b) Find the number of pencils that Jeremy can buy with $20.
11) The figure shown is formed by a rectangle and a square. Express the area of the
figure in terms of x. (Area = length • width)
Homework 3
Practice 7.2 – Evaluating Algebraic Expressions
Evaluate each expression for the given value of the variable.
1) x + x + 5 when x = 7
2) 3x + 5 when x = 5
3) 5y – 8 when y = 3
4) 40 – 9y when y =2
5) 33 – 7w + 6 when w = 4
6)
7w
when w = 18
6
8)
4  5z
when z = 12
6
7) 4 
5z
when z = 12
6
9) 20 
4r
when r = 10
5
11) 16 
2z  4
when z = 18
3
10)
8r
 15 when r = 27
9
12) 16 
2z
 4 when z = 18
3
Homework 4
Evaluate each expression when x = 3.
13)
x  1 5x  3

2
10
14)
15)
7x  6
 4(8  2 x)
3
16) 13(11  3 x) 
17) 5( x  2)  2(6  x ) 
19)
2x  4 x  1 x


5
4
6
2x  3
3
18)
11  x 9 x  3

2
4
5(16  4 x)
2
5 x  3 5( x  5)

 3(13  2 x)
4
8
20) 7 x 
x 7x

5
9
Homework 5
Evaluate each of the following when y = 7.
y
4y
and
3
9
21) (5y + 2) minus (2y + 5)
22)The sum of
23) The product of (y + 1) and (y – 1)
24) 8(2y – 1) minus
25) The quotient of 9(7y – 15) and
110  6 y
4
 y 2y 
 5y y 

 
 and 
3 
2
 6 3
26) The quotient of 
26)The sum of
14 y  37
5
5y
and
6
 3y

4
 2y
 7

Homework 6
Practice 7.3 – Simplifying Algebraic Expressions
Simplify each expression. Then state the coefficient of the variable.
1) u + u + u + u
2) v + v + 5 – 2
_____________
_____________
_____________
coefficient: _____
coefficient: _____
coefficient: _____
3) w + w + w + w + w + w + 15 - 7
Simplify each expression.
4) 3p + p
7) 3p – 2p + 5p
5) 4p + 5p
6) 7p – 2p
8) 2p + 3p + 4p + 5p – 6p – 7p
Simplify first, then state whether each pair of expressions are equivalent.
9) 5x and x + x + 3x
10) 4y + 2y + y and 5y + y
11) 2z + 5 and z + 8 + z – 3
12) 2w – 5 and 5 – 2w
13) 11u – 4u and 11 – 4 + u
14) 3v + v and
12v
3
Homework 7
Simplify each expression.
15) 3x + 5 + 4x + 6
16) 3x + 2x + 3x + 2
17) 17 + 4w – 12 – w
18) 9 + 5u + 6u – 7 – 8u + 4
Solve.
19) A book has a length of (w + 2) inches and a width of w inches. Label the picture.
Write a simplified expression for the perimeter of the book.
20) The figure shows a quadrilateral. The length of each side is given as shown. Find
the perimeter of the quadrilateral in terms of z.
Homework 8
21) Anne is currently a years old. Bill is currently 2a years old and Charles is currently 8
years old.
a) Find an expression for each person’s age after a years.
b) Find an expression for the sum of their ages after a years.
23) A rectangular garden has a length of (y + 2) yards and width of (4y – 1) yards. Find
the perimeter of the garden in terms of y.
24) Kayla had 64d dollars. She gave
1
of it to Luke and spent $45. How much money
8
did Kayla have left? Express your answer in terms of d.
Homework 9
25) A rectangle has a length of (2m + 1) units and a width of (10 – m) units.
A square has sides of length
2m + 1
units.
2
a) Find the perimeter of the rectangle.
b) Find the perimeter of the square.
c) Find the sum of the perimeter of the two figures if m = 6.
d) If m = 6, the perimeter of the rectangle is greater than the perimeter of the square.
Find how many units greater.
Homework 10
Practice 7.4 – Expanding and Factoring Algebraic Expressions
Expand each expression.
1) 5(x + 2)
2) 7(2x – 3)
3) 4(y – 3)
4) 8(3y – 4)
5) 3(x + 11)
6) 9(4x – 7)
Factor each expression. (Factor out the GCF)
7) 6p + 6
8) 3p + 18
9) 12 + 3q
10) 4w – 16
11) 14r – 8
12) 12r – 12
State whether each pair of expressions are equivalent. (Expand first.)
13) 4x + 12 and 4(x + 3)
14) 5(x – 1) and 5x – 1
15) 7(5 + y) and 7y + 35
16) 9(y – 2) and 18 – 9y
Homework 11
Expand and simplify each expression. (Expand = distributive property.)
17) 3(m + 2) + 4(6 + m)
18) 5(2p + 5) + 4(2p – 3)
19) 4(6k + 7) + 9 – 14k
Expand and simplify each expression. Then factor the expression.
(Expand = distributive property.)
20) 14x + 13 – 8x – 1
22) 4(3z + 7) + 5(8 + 6z)
21) 8(y + 3) + 6 – 3y
Homework 12
Solve.
23) Expand and simplify the expression 3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).
24) Are the two expressions equivalent? Justify your reasoning.
15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)
25) A yard of lace costs c cents and yard of fabric costs 40ȼ more than the yard of lace.
Kimberly wants to buy one yard of lace and 2 yards of fabric. How much money will she
need? Express your answer in terms of c.
26) The average weight of 6 packages is (9p + 8) pounds. 2 more packages, with
weights of (12p + 12) pounds and (14p + 12) pounds, are added to the original 6
packages. Find the average weight of the 8 packages.
Homework 13
27) The figure shows two rectangles joined to form rectangle ABCD.
a) Write the length of
BC in terms of x.
Then write an expression for the area of the rectangle ABCD in terms of x.
b) Write an expression for the area of each of the two smaller rectangles.
White Rectangle
Black Rectangle
c) How can you use your answer in a) and b) to show that the following expressions are
equivalent?
3x + 6 and 3(x + 2)
Homework 14
Practice 7.5 – Real-World Problems: Algebraic Expressions
Solve. Show your work.
1) Jenny is j years old. Thomas is 3 times as old as she is. Jenny is 5 years older than
Alexis.
a) Find Alexis’s age in terms of j.
b) Find Thomas’s age in terms of j.
c) If j = 12, how much older is Thomas than Jenny?
2) A van travels from Town A to Town B. It uses 1 gallon of gas for every 24 miles
traveled.
a) How many gallons of gas does the van use if it travels 3 miles?
b) The van uses 2 gallons of gas for its journey from Town A to Town B. Find the
distance between Town A and Town B.
Homework 15
Draw a picture to help you solve.
4) A rectangle has a width of x centimeters and perimeter of 8x centimeters.
A square has sides of length
1
that of the length of the rectangle.
4
a) Find the length of the rectangle.
b) Find the perimeter of the square.
c) Find how many centimeters greater the rectangle’s perimeter is than the square’s
perimeter if x = 4.
d) Find how many square centimeters greater the rectangle’s area is than the square’s
area if x = 4. (Area = length • width)
Homework 16
5) Jose bought 4 comic books and 2 nonfictions books. The comic books cost him 8d
dollars. If the cost of one nonfiction book is (3 + 7d) dollars more expensive than the
cost of one comic book, find
a) the cost of the 2 nonfiction books in terms of d.
b) the total amount that Jose spent on the books if d = 4.
Homework 17
6) Wyatt has (2d – 1) one-dollar bills and (4d + 2) five-dollar bills. Susan has 3d dollars
more than Wyatt.
a) Find the total amount of money that Wyatt has in terms of d.
b) Find the number of pens that Wyatt can buy if each pen costs 50 cents. Express in
terms of d.
c) If d = 21, find how much money Susan will have now if Wyatt gives her half of the
number of five-dollar bills that he has.