Download Algebra 2 - Rochester Community Schools

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Algebra II
1.3 & 1.6 Worksheet
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Date ______________________Hour ____
1.3 – Solving Equations
Solve the equation.
1
a  5
1. 6m  3  21
2.
4. 5 x  4  2 x  8
5. 2c  14  6  4c
7.
10.
3m  5  6m  1
1
2
x 
1
3
x  10
8.
11.
1
3
3. 4 x  7   15
10 w  4  4 w  4  4w
3
7
x
2
9
 94 x 
1
7
12. The perimeter of the rectangle is 46 inches. Find its dimensions.
6. 17  6 w  25  3w
9.
32x  5  x   7x  3
Solve the equation . (If there is no solution, write no solution. If the equation is always true, write all real numbers).
13.
5 2  x  3  2x  7  3x
14.
 2 4  3x  7  6 x 1
15. You are ordering T-shirts from a catalog. Each
T-shirt costs $15. The cost of shipping is $6 no
matter how many you order. The total cost is
$111. How many T-shirts did you order?
16. The bill for the repair of your bicycle was $180.
The cost of parts was $105. The cost of labor
was $25 per hour. How many hours did the
repair work take?
17. Your friend bought a total of 10 CDs and DVDs
as gifts for $199. The price per CD was $15 and
the price per DVD was $22. Write and solve an
equation to find how many CDs and how many
DVDs your friend bought.
18. You have two summer jobs. In the first job, you
work 25 hours per week and earn $7.75 per hour.
In the second job, you earn $6.25 per hour and
can work as many hours as you want. You want
to earn $250 per week. How many hours must
you work at the second job?
19. It takes you 30 minutes to rake the leaves in your
yard and it takes your brother 45 minutes. How
long does it take the two of you to rake the
leaves when working together?
20. You paint 2 square yards of a community mural
in 3 hours and a friend paints 4 square yards in 5
hours. How long does it take the two of you to
paint 11 square yards when working together?
(see Ex 3 from the 1.3 notes)
(see Ex 3 from the 1.3 notes)
1.6 – Solving Inequalities
21. Write the compound inequality that is represented by the graph.
a)
b)
Solve the inequality. Then graph the solution.
4  32 x  13
22. 15  3 x  3
23.
24. 21x  7  3 x  16
25. 2  3 x  1  11
26.  3  4  x  3
27. x  1   3 or x  2  0
Solve the inequality. (If there is no solution, write no solution. If the inequality is always true, write all real numbers).
28.
23x  1  32x  3
30. You have budgeted $100 to improve your
swimming over the summer. At your local pool, it
costs $50 to join the swim association and $5 for
each swim class. Write and solve an inequality to
find the possible numbers of swim classes you
can attend within your budget.
29.
4 x  5  4x  2
31. On a certain highway there is a minimum speed of
45 miles per hour and a maximum speed of 70 miles
per hour.
a) Write a compound inequality for the legal
speeds on the highway.
b) Write a compound inequality for the illegal
speeds on the highway.
32. Multiple Choice. Canoe rental costs $18 for the
first two hours and $3 per hour after that. You
want to canoe for more than 2 hours but can
spend no more than $30. Which inequality
represents the situation, where t is the total
number of hours you can canoe?
18  3t  2  30
B) 18  3t  2  30
C) 18  t  30
D) 18  3t  30
A)
33. Your final grade in a course is 65% of your
homework score, 15% of your quiz score, and 20%
of your final exam score. (All scores range from 0 to
100). Your homework score is 84 and your quiz
score is 80. Write and solve an inequality to find the
possible final exam scores that result in a grade of
85 or better.