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```Name ———————————————————————
LESSON
3.4
Date ————————————
Practice A
For use with pages 154 –160
1. 10x 2 7 5 4x 1 5
2. 3x 1 6 5 22x 1 11
A. 6x 2 7 5 5
A. 5x 1 6 5 11
3. 6(3x 2 4) 5 12
A. 18x 2 24 5 12
B.
6x 5 12
B.
5x 5 5
B.
18x 5 36
C.
x52
C.
x51
C.
x52
4. 6(x 1 3) 5 5x 1 8
5. 4(x 2 2) 5 7x 1 1
A. 6x 1 18 5 5x 1 8
B.
C.
6. 2x 1 2 5 4(x 2 5)
A. 4x 2 8 5 7x 1 1
x 1 18 5 8
x 5 210
LESSON 3.4
Describe each step used in solving the equation.
A. 2x 1 2 5 4x 2 20
B.
28 5 3x 1 1
B.
2 5 2x 2 20
C.
29 5 3x
C.
22 5 2x
D.
23 5 x
D.
11 5 x
Solve the equation and describe each step you use.
7. 6p 2 3 5 4p 2 1
8. 10a 2 2 5 7a 1 4
9. 5(m 1 2) 5 20
Solve the equation, if possible.
10. 9x 2 2 5 8x 1 7
11. 5n 2 3 5 3n 1 1
12. 4z 2 5 5 8z 1 3
13. 2a 1 4 5 a 1 6
14. w 1 8 5 w 2 3
15. 2( y 2 3) 5 y 1 4
16. 3(m 1 2) 5 8 1 m
17. 6 1 x 5 6(x 2 5)
18. 7(b 1 3) 5 7b 2 4
19. Dimensions of a Circular Flower Garden A ﬂower garden has
the shape shown. The diameter of the outer circle is three times
the diameter of the inner circle. The lengths of the walkways are
8 feet long. What is the diameter of the inner circle?
x
8 ft
8 ft
3x
20. Distance-Rate-Time Two cars travel the same distance. The ﬁrst car travels at a rate
of 50 miles per hour and reaches its destination in t hours. The second car travels at
a rate of 60 miles per hour and reaches its destination 1 hour earlier than the ﬁrst car.
How long does it take for the ﬁrst car to reach its destination?
Rate of
car 1
p
Time for
car 1
5
Rate of
car 2
p
Time for
car 2
Algebra 1
Chapter 3 Resource Book
41
Name ———————————————————————
Practice B
LESSON
3.4
LESSON 3.4
Date ————————————
For use with pages 154 –160
Solve the equation and describe each step you use.
1. 5x 1 11 5 4x 1 18
2. 11p 2 4 5 6p 1 1
3. 26 5 2(w 1 5)
Solve the equation, if possible.
4. 15x 2 8 5 14x 1 13
5. 9n 2 7 5 5n 1 5
6. 4z 2 15 5 4z 1 11
7. 27a 1 9 5 3a 1 49
8. 4(w 1 3) 5 w 2 15
9. 8( y 2 5) 5 6y 2 18
10. 14m 2 10 5 3(4 1 m)
1
11. 7 1 x 5 } (4x 2 2)
2
12. 8b 1 11 2 3b 5 2b 1 2
13. 10d 2 6 5 4d 2 15 2 3d
14. 16p 2 4 5 4(2p 2 3)
15. 0.25(8z 2 4) 5 z 1 8 2 2z
Find the perimeter of the square.
16.
17.
18.
5x ⫺ 8
3x
7x ⫺ 15
10x
6x 1 8
2x
19. Saving and Spending Currently, you have \$80 and your sister has \$145. You decide
20. Botanical Gardens The membership fee for joining a gardening association is
\$24 per year. A local botanical garden charges members of the gardening association
\$3 for admission to the garden. Nonmembers of the association are charged \$6.
After how many visits to the garden is the total cost for members, including the
membership fee, the same as the total cost for nonmembers?
21. College Enrollment Information about students’ choices of majors at a small
college is shown in the table. In how many years will there be 2 times as many
students majoring in engineering than in business? In how many years will there be
2 times as many students majoring in engineering than in biology?
Major
42
Number of students enrolled in major
Average rate of change
Engineering
120
22 more students each year
105
4 fewer students each year
Biology
98
6 more students each year
Algebra 1
Chapter 3 Resource Book
to save \$6 of your allowance each week, while your sister decides to spend her
whole allowance plus \$7 each week. How long will it be before you have as much
Name ———————————————————————
LESSON
3.4
Date ————————————
Practice C
For use with pages 154 –160
1. 9x 2 4 5 7x 2 16
2. 5d 2 3 1 2d 5 4d 1 9
3. 4(2m 1 5) 5 3m 2 5
4. 6(7 2 2p) 5 3(5p 1 1)
5. 11w 1 2(w 1 1) 5 5w 2 6
6. 10 1 2(2a 1 1) 5 7a 2 3
1
7. } (12n 2 2) 5 5n 2 7
2
1
8. 4y 1 16 5 } (10y 2 4)
3
3
9. 2} (8x 2 12) 5 5x 2 2
4
LESSON 3.4
Solve the equation and describe each step you use.
Solve the equation, if possible.
10. 42n 2 13 5 17n 1 12
11. 4.5x 1 3.4 5 1.5x 2 2.6
12. 14d 2 43 5 6d 2 13 2 7d
13. 24(2w 2 5) 5 3w 2 13
14. 14 2 4z 5 2(17 2 z)
15. 9(4h 2 6) 5 2(213 2 2h)
3
1
2
1
16. } x 1 } 5 } x 2 }
2
3
3
2
1
17. } (6x 1 3) 5 2x 2 5
3
1
1
18. } (9 2 2x) 5 } (3x 1 4)
8
4
19. 6.8t 2 10 2 3.2t 5 3t 2 1
20. 6(1.3p 2 3) 5 2.6p 2 5
21. 0.2(15z 2 5) 5 4(4z 1 1)
Find the length and the width of the rectangle described.
22. The length is 5 units more than the width. The perimeter is 9 times the width.
23. The length is 5 units less than 2 times the width. The perimeter is 22 units more than
twice the width.
24. High School Enrollments Central High’s enrollment decreases at an average rate
of 55 students per year, while Washington High’s enrollment increases at an average
rate of 70 students per year. Central High has 2176 students and Washington High
has 1866 students. If enrollments continue to change at the same rate, when will the
two schools have the same number of students?
25. Teeter-Totter Two children weighing 42 pounds and
54 pounds are on a teeter-totter as shown. The 54-pound
child is sitting 1 foot closer to the center than the 42-pound
child. To balance the teeter-totter, the 42-pound child must
sit x feet from the center. Write an equation to ﬁnd how
many feet the 42-pound child must be from the center of
the teeter-totter so it is balanced. Solve for x.
54 lb
42 lb
x⫺1
x
26. Charity Race In a 5-mile charity race, groups of runners are started 5 minutes
apart. One runner in the ﬁrst group is running at a rate of 0.06 mile per minute.
One runner in the second group is running at a rate of 0.1 mile per minute.
a. Let t represent the time (in minutes) it takes the runner from the ﬁrst group to
run the race. Write and solve an equation to ﬁnd the number of minutes after
which the runner from the second group would catch up with the runner from
the ﬁrst group.
b. Does the runner from the second group pass the runner from the ﬁrst group
before the race is over? Explain your reasoning.
Algebra 1
Chapter 3 Resource Book
43
Name ———————————————————————
LESSON
3.4
Date ————————————
Challenge Practice
For use with pages 154 –160
LESSON 3.4
1. For what value of a is a(x 2 5) 5 9x 2 25 2 2x 2 10 an identity?
2. For what value of b is 2x 2 bx 2 3 5 b(2x 2 3) 213x 1 12 an identity?
3. For what value of c is 2(cx 1 12) 5 3(cx 1 8) an identity?
4. For what value of d is d(dx 1 1) 5 24dx 2 2d 2 12 an identity?
5. Find the area of a rectangle whose perimeter is 34 inches and whose width is two
more than twice the length.
6. Find the area of a rectangle whose length is 6 inches less than 5 times the width
and whose perimeter is 8 inches more than twice the length.
7. Find the area of a rectangle whose length is one-third of the perimeter, whose width
is one-half of the length, and whose perimeter is 60 inches.
8. Find the length of a rectangle which when cut in half has an area of 300 square
inches and whose width is one-sixth of the length.
Algebra 1
Chapter 3 Resource Book
49
Name ———————————————————————
LESSONS
3.1–3.4
Date ————————————
Problem Solving Workshop:
Mixed Problem Solving
For use with pages 134–159
rectangle is 12 inches greater than the width.
The perimeter of the rectangle is 48 inches.
a. Write a verbal model for the situation.
a. Write and solve an equation to ﬁnd the
b. Use the verbal model to write and solve
dimensions of the rectangle.
b. What is the area of the rectangle?
c. Suppose the length and width are
doubled. What affect does this have on
the perimeter and area of the rectangle?
an equation. How many shirts did you
c. What was the average cost per shirt?
2. Multi-Step Problem Your kitchen ﬂoor
is 30 feet long and 18 feet wide. You want to
cover the kitchen ﬂoor with square tiles that
have a side length of 3 feet.
a. Find the area of one tile.
b. Write an equation for the number of tiles
that will cover the kitchen ﬂoor.
c. How many tiles are needed to cover the
kitchen ﬂoor?
3. Gridded Answer Each side of the
6. Extended Response The length of a
for \$12 per shirt. Every shirt after the second
shirt is \$4 off. You spent \$56.
triangle has the same length. The perimeter
of the triangle is how many units?
2x 1 7
3x 1 4
4. Short Response A basketball team plays
20 games and averages 58 points per game.
Write a verbal model for ﬁnding the total
number of points for the season. Write and
solve an algebraic model. The team’s goal
for next year is to score 5 more points per
game for 20 games. How many total points
does the team want to score next year?
5. Gridded Answer Mike weighs 110
pounds. He weighs 23 pounds more than
Brian. How many pounds does Brian weigh?
LESSON 3.4
1. Multi-Step Problem You bought n shirts
7. Open-Ended Write an equation that can
be solved using only addition. Write an
equation that can be solved using only
multiplication. Write a two-step equation
that can be solved using addition
and multiplication.
8. Extended Response In basketball, a
player’s ﬁeld goal percentage is calculated
by dividing the number of ﬁeld goals made
by the number of ﬁeld goals attempted.
Player
Steve Nash
Team
Phoenix Suns
Field goal percentage
0.502
Field goals attempted 857
a. Use the information in the table to
ﬁnd the number of ﬁeld goals made by
Steve Nash in the 2004–2005 National
whole number.
b. Tony Parker of the San Antonio Spurs
made 109 more ﬁeld goals than Steve
Nash in the 2004–2005 regular season.
How many ﬁeld goals did Tony Parker
make?
c. In the 2004–2005 regular season, Steve
Nash had a higher ﬁeld goal percentage
than Tony Parker. Did Tony Parker have
fewer attempts than Steve Nash? Explain
Algebra 1
Chapter 3 Resource Book
47
Name ———————————————————————
LESSON
3.4
Date ————————————
Investigating Algebra Activity: Modeling
Equations with Variables on Both Sides
For use before Lesson 3.4
QUESTION
EXPLORE
algebra tiles
How can you use algebra tiles to solve an equation with a variable
on both the left and the right side of the equation?
LESSON 3.4
Materials:
Solve an equation with variables on both sides
Solve 5x 1 4 5 3x 1 8.
STEP 1 Model 5x 1 4 5 3x 1 8
using algebra tiles.
STEP 2 You want to have x-tiles on
only one side of the equation, so
subtract three x-tiles from each side.
5
5
STEP 3 To isolate the x-tiles, subtract
four 1-tiles from each side.
STEP 4 There are two x-tiles, so
divide the x-tiles and 1-tiles into two equal
groups. So, x 5 2.
5
5
DRAW
CONCLUSIONS
Use algebra tiles to model and solve the equation.
1. 4x 1 3 5 3x 1 7
2. 2x 1 8 5 11 1 x
3. 5x 1 9 5 8x 1 6
4. 7x 1 6 5 9x 1 2
5. Copy and complete the equations and explanations.
2x 1 19 5 7x 1 4
2x 1 19 2 ?
5 7x 1 4 2 ?
19 5 ?
19 2 ?
14
Original equation
Subtract ? from each side.
Simplify.
5 5x 1 4 2 ?
Subtract ? from each side.
?
5 5x
Simplify.
?
5x
Divide each side by ? and simplify.
Algebra 1
Chapter 3 Resource Book
39
Name ———————————————————————
LESSON
LESSON 3.4
3.4
Date ————————————
Study Guide
For use with pages 154 –160
GOAL
Solve equations with variables on both sides.
Vocabulary
An equation that is true for all values of the variable is an identity.
EXAMPLE 1
Solve an equation with variables on both sides
Solve 13 2 6x 5 3x 2 14.
Solution
13 2 6x 5 3x 2 14
Write original equation.
13 2 6x 1 6x 5 3x 2 14 1 6x
13 5 9x 2 14
Simplify.
27 5 9x
35x
Divide each side by 9.
The solution is 3. Check by substituting 3 for x in the original equation.
13 2 6x 5 3x 2 14
Write original equation.
13 2 6(3) 5 3(3) 2 14
Substitute 3 for x.
25 5 3(3) 2 14
Simplify left side.
25 5 25 ✓
Simplify right side. Solution checks.
Exercises for Example 1
Solve the equation. Check your solution.
1. 9a 5 7a 2 8
EXAMPLE 2
2.
17 2 8b 5 3b 2 5
3. 25c 1 6 5 9 2 4c
Solve an equation with grouping symbols
1
Solve 4x 2 7 5 }
(9x 2 15).
3
Solution
1
4x 2 7 5 }3 (9x 2 15)
Write original equation.
4x 2 7 5 3x 2 5
Distributive property
x 2 7 5 25
x52
The solution is 2.
44
Algebra 1
Chapter 3 Resource Book
Subtract 3x from each side.
CHECK
Name ———————————————————————
LESSON
3.4
Study Guide
Date ————————————
continued
For use with pages 154 –160
LESSON 3.4
Exercises for Example 2
Solve the equation. Check your solution.
4. 2m 2 7 5 3(m 1 8)
1
5. } (15n 1 5) 5 8n 2 9
5
3
6. 7p 2 3 5 } (8p 2 12)
4
EXAMPLE 3
Identify the number of solutions of an equation
Solve the equation, if possible.
a. 4(3x 2 2) 5 2(6x 1 1)
b. 4(4x 2 5) 5 2(8x 2 10)
Solution
a. 4(3x 2 2) 5 2(6x 1 1)
12x 2 8 5 12x 1 2
12x 5 12x 1 10
Write original equation.
Distributive property
The equation 12x 5 12x 1 10 is not true because the number 12x cannot be
equal to 10 more than itself. So, the equation has no solution. This can be
demonstrated by continuing to solve the equation.
12x 2 12x 5 12x 1 10 212x
0 5 10
Subtract 12x from each side.
Simplify.
The statement 0 5 10 is not true, so the equation has no solution.
b. 4(4x 2 5) 5 2(8x 2 10)
16x 2 20 5 16x 2 20
Write original equation.
Distributive property
Notice that the statement 16x 2 20 5 16x 2 20 is true for all values of x. So, the
equation is an identity.
Exercises for Example 3
Solve the equation, if possible.
7. 11x 1 7 5 10x 2 8
8. 5(3x 2 2) 5 3(5x 2 1)
1
9. } (6x 1 18) 5 3(x 1 3)
2
Algebra 1
Chapter 3 Resource Book
45
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