Algebra 1Hmk #41
Name:___________________________________
Review: Inequalities – Solving and graphing
Date:______________
Block:_______________
Solve each inequality, then math the inequality with the graph of its solution set.
1.
2.
3.
4.
5.
–y < -2 _____
–y < 2 _____
3y > -6 _____
-3y > -6 _____
y – 1 > 1 _____
___
___
___
___
___
A)
B)
C)
D)
E)
Solve the inequality, and graph the solution set.
6) 3 – 2(3x + 2) < 1 + 2(3x – 4) ________
-5
-4
-3
-2
-1
0
1
2
3
7) 8 < 2x – 8(x – 1)
4
-5
5
-4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
2
9)   x  5   4
3
8) 8 – 3(x + 4) < -x – 6 ________
-5
-4
__________
5
-5
-4
-3
-2
-1
1
2
3
4
5
________
0
1
2
3
4
5
3
(16  8x )  4 x  2 ________
8
10)
-5
-4
-3
-2
-1
0
1
2
3
11)
4
5
3
3
x 2  x 5
4
2
-5
-4
-3
-2
-1
0
1
2
3
4
5
Graph each inequality.
12) y  3x  1
13) y 
y
1
x
2
y
x
14) x  2y  4
x
15) 3x  y  3
y
x
y
x
Graph the system of linear inequalities, and indicate the solution set of the system with shading!
y  2x  3
16)
1
y   x 2
2
y
17)
x y 3
2x  y  6
y
x
x
17 a) Name a solution to the system:_______
y
17 b) Name one point that is not a
solution to the system: ________
y  x 2
18) x  1
y 5
x
WORD PROBLEMS: Directions:
1) Set up each probable by defining the variable
2) Write an inequality based on each situation.
3) Solve the inequality.
4) Answer the WORD PROBLEM in a COMPLETE sentence!
19) You can work at most 24 hours per week as a nurse’s aid. So far this week you have worked 7 hours. If the
remaining shifts for the week are each 4 hours long, how many possible shifts can you work?
20) You scored the following points in four basketball games: 16, 24, 32, and 22. After the next game, you want
your average score to be at least 25 points per game after your fifth game. What are the possible scores that you
can earn in your next game in order to meet your goal?
21) A blank CD can hold 70 minutes of music. So far you have burned 25 minutes of music onto the CD. You
estimate that each song lasts 4 minutes. What are the possible number of total songs that can be burned onto
the CD?
22) A zookeeper is designing a rectangular habitat for swans, 20 ft by 50 ft. The zookeeper needs to reserve 500
square feet for the first 2 swans and 125 square feet for each additional swan. What are the possible number of
swans that the habitat can hold?
23) A gym is offering a trial membership for 3 months by discounting the regular monthly rate by $50. You will
consider joining the gym if the total cost of the trial membership is less than $100. Which inequality can you use
to find the possible regular monthly rates that you are willing to pay?
A) 3x – 50 < 100
B) 3x – 50 > 100
C) 3(x – 50) < 100
D) 3(x – 50) > 100