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WorksheetsWrite and Solve Two-Step Inequalities
Total questions: 62
Worksheet time: 5hrs 29mins
Name
Class
Date
1.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥
2.
Match the graph with its inequality.
a)
a > 11
b)
a < 11
c)
a ≥ 11
d)
a ≤ 11
3.
What inequality does the number line graph represent?
a)
x ≤ -4
b)
x ≥ -4
c)
x < -4
d)
x < 4
4.
Pick the correct inequality.
a)
A
b)
B
c)
C
d)
D
5.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥
b)
<, >
6.
Write an inequality for this situation:
You are driving, and the maximum speed limit is 55.
You are driving, and the maximum speed limit is 55.
a)
s < 55
b)
s > 55
c)
s ≤ 55
d)
s ≥ 55
7.
3g >12
a)
g>36
b)
g<36
c)
g>4
d)
g<4
8.
x/4≤8
a)
x≤2
b)
x≤32
c)
x≤12
d)
x≤4
9.
Solve the inequality.
x + 5 ≤ 13
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8
d)
x ≤ 18
10.
To order from the kids menu a person must be no more than 12 years old.
a)
x > 12
b)
x < 12
c)
x ≥ 12
d)
x ≤ 12
11.
Match:
You must be at least 48 inches tall to ride the bumper cars.
You must be at least 48 inches tall to ride the bumper cars.
a)
h < 48
b)
h > 48
c)
h ≤ 48
d)
h ≥ 48
12.
Is 7 a solution to the inequality below?
d + 2 < 6
d + 2 < 6
a)
Yes
b)
No
13.
Is 9 a solution to the inequality below?
4k ≥ 36
4k ≥ 36
a)
Yes
b)
No
14.
Which number is a possible solution to the inequality below?
12 - m ≤ 7
12 - m ≤ 7
a)
8
b)
9
c)
5
d)
all three are possible solutions
15.
Solve for t.
6t + 4 ≤ -2
6t + 4 ≤ -2
a)
t ≤ -1
b)
t ≤ 1
c)
t=1
d)
1=t
16.
Solve for k.
7k – 2 ≥ -9
7k – 2 ≥ -9
a)
k ≤ -1
b)
k≤1
c)
k≥1
d)
k ≥ -1
17.
Solve for k.
2k - 9≤ -19
2k - 9≤ -19
a)
k ≤ -5
b)
k ≤ 5
c)
k < -5
d)
k < 5
18.
16 - 4a > 8
a)
a<-2
b)
a>-2
c)
a<2
d)
a>2
19.
-9a - 1 < 26
a)
a<-3
b)
a<3
c)
a>-3
d)
a>3
20.
You order a new pair of running shoes from a website that offers free shipping on orders of $75 or more. Your shoes cost $69.95. Write and solve an inequality that represents how much more you must spend to get free shipping.
a)
X > 5.05
b)
X ≥ 5. 05
c)
X > 69.95
d)
X ≥ 69.95
21.
4. A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel? (Note: The taxi driver will charge for the next mile once he goes over)
a)
10 miles
b)
12 miles
c)
14 miles
d)
16 miles
22.
Solve for t.
6t + 4 ≤ -2
6t + 4 ≤ -2
a)
t ≤ -1
b)
t ≤ 1
c)
t=1
d)
1=t
23.
Solve for k.
7k – 2 ≥ -9
7k – 2 ≥ -9
a)
k ≤ -1
b)
k≤1
c)
k≥1
d)
k ≥ -1
24.
You flip an inequality symbol when you...
a)
subtract
b)
multiply and divide only
c)
multiple by a negative number
d)
multiple or divide by a negative number
25.
When graphing b < 6 would you use an open or closed circle?
a)
Open
b)
closed
26.
Pick the correct letter for:
6 > x
6 > x
a)
A
b)
B
c)
C
d)
D
27.
Do I need to flip my sign?
-3x ≥ 12
-3x ≥ 12
a)
Yes
b)
No
28.
-75 + 50x < 125
a)
x < 4
b)
x > 4
c)
x < 10
d)
x > 10
29.
-12x + 1 > -47
a)
x > 4
b)
x < 4
c)
x < -4
d)
x > -4
30.
Jim paid a gym membership fee of $50, plus $20 per month. Jim has paid a total of $290 to the gym. How many months has he been a member at the gym?
a)
12
b)
17
c)
64.5
d)
15
31.
Last Friday Samantha had $22.50. Over the weekend, she received some money for cleaning. She now has more than $32.00. Which inequality represents this situation?
a)
22.50 - x > 32
b)
22.50x > 32
c)
22.50 + x > 32
d)
22.50 +x < 32
32.
Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?
a)
10x + 1.50 ≥ 40
b)
1.50x + 10 ≤ 40
c)
1.50x + 10 <40
d)
10x + 1.50 < 40
33.
The temperature in the ice rink must stay below 50°F. This morning, the temperature was 71°F. The ice rink runs a cooling device that can decrease the temperature by 3.5° every hour. Which inequality shows how long it will take for the temperature to fall below 50°F?
a)
50 + 3.5x < 71
b)
71 - 3.5x < 50
c)
71 - 3.5x ≤ 50
d)
71 + 3.5x < 50
34.
Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?
a)
200 + 25x ≥ 500
b)
500 + 25x ≥ 200
c)
500 - 25x ≥ 200
d)
500 - 25x ≤ 200
35.
The members of Carver Middle School's Junior Beta Club need to raise at least $2000 to attend their national convention. They raised $300 with their last fundraiser and decide to host a school talent show to raise the rest. They plan to charge $10 for each ticket. Which inequality shows the number of tickets they must sale to reach their goal?
a)
300x + 10 ≥ 2000
b)
10x + 300 ≤ 2000
c)
10x + 300 > 2000
d)
300 + 10x ≥ 2000
36.
The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?
a)
106 - 4x ≤ 70
b)
70 + 4x ≤ 106
c)
4x - 106 ≥ 70
d)
106 - 4x< 70
37.
It costs Amy $0.20 to send a text message. She has already spent $5 in text messages this month. If she has a total of $12 that can spend this month on text messages, write and solve an inequality that will give the greatest number of text messages that she can send.
a)
0.20x + 5 = 12;
85 text messages
85 text messages
b)
0.20(5x) = 12;
12 text messages
12 text messages
c)
0.20x + 5 ≤ 12;
x ≤ 35
x ≤ 35
d)
0.20x + 5 ≥ 12;
x ≥ 35
x ≥ 35
38.
Which situation can be represented by the inequality
15 + 6x ≤ 100?
15 + 6x ≤ 100?
a)
Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?
b)
Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?
c)
Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?
d)
Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?
39.
Which word problem represents the inequality:
x + 32 ≥ 80
(Show work by writing down inequality clue words.)
x + 32 ≥ 80
(Show work by writing down inequality clue words.)
a)
Janine's goal is to earn at least $80 for soccer camp. She has earned $32 so far. How much more does she need to earn?
b)
Janine made more than 80 points during the basketball season. She made 32 points the first five games. How much did she score the rest of the games?
c)
Janine scored above an 80 on her math homework. But, she turned her work in late and was deducted 32 points. What did she make after the deduction?
40.
Pheobe has $500 in a savings account at the beginning of the summer. She wants to have at least $200 in account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Write an inequality that represents Pheobe's situation.
a)
200+25w ≥ 500
b)
500-25w ≥ 200
c)
500+25w ≤ 200
d)
200-25w ≤ 500
41.
Match the inequality to the word problem.
Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks. How many dogs would Katie have to walk to reach her goal of $200?
a)
25 - 12x ≥ 200
b)
25 + 12x ≥ 200
c)
13x ≥ 200
d)
25 + 12x > 200
42.
Who is this....
a)
Clifford
b)
Scooby Doo
c)
Snoopy
d)
Odie
43.
Greater than
a)
<
b)
>
c)
≤
d)
≥
44.
Less Than
a)
<
b)
>
c)
≤
d)
≥
45.
Less than or equal to
a)
<
b)
>
c)
≤
d)
≥
46.
Greater than or equal to
a)
<
b)
>
c)
≤
d)
≥
47.
x + 5 < 6
a)
x < 1
b)
x > 1
c)
x < 11
d)
x > 11
48.
Solve the inequality.
x + 5 ≤ 13
x + 5 ≤ 13
a)
x ≥ 8
b)
x ≥ 18
c)
x ≤ 8
d)
x ≤ 18
49.
What inequality does the number line graph represent?
a)
x > 5
b)
x < −5
c)
x ≥ 5
d)
x ≥ −5
50.
Match the graph with its inequality.
a)
a > 11
b)
a < 11
c)
a ≥ 11
d)
a ≤ 11
51.
When you graph an inequality, you use a closed dot when you use which symbols?
a)
≤, ≥
b)
<, >
c)
≤, <
d)
≥, >
52.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥
c)
≤, <
d)
≥, >
53.
What are two solutions to x < 8?
a)
8.6, 7.9
b)
11, 16
c)
0.8, 5.9
d)
12, 7.1
54.
Write an inequality for this situation:
You are driving, and the maximum speed limit is 55.
You are driving, and the maximum speed limit is 55.
a)
s < 55
b)
s > 55
c)
s ≤ 55
d)
s ≥ 55
55.
Mr. Gomez gets a notice from the bank when the amount in his checking account drops below $20. Which represents an amount that will require the bank to send a notice?
a)
$18
b)
$19
c)
$20
d)
$21
e)
$22
56.
You must spend at least $10 at the grocery store to get a free reusable shopping bag. Which inequality represents the amount you need to spend to get a free shopping bag?
a)
x<10
b)
x>10
c)
x>10
d)
x<10
57.
When the following inequality is graphed, what will it look like?
y>-1
a)
open circle
b)
closed circle
58.
When the following inequality is graphed, what will it look like?
r < -12.97
a)
open circle
b)
closed circle
59.
List the integers graphed on the number line from least to greatest.
a)
-4, 0, 2, 5
b)
-5, -4, -3, -2, -1
c)
-5, -3, 0, 3, 5
d)
5, 2, 0, -4
60.
When do you "flip the inequalities sign"?
a)
When you add or subtract a negative
b)
When it's a 1-step problem
c)
When you multiply or divide a negative
d)
When it's a 2-step problem
61.
2x > 12
a)
x > 6
b)
x < 6
c)
x ≥ 6
d)
x ≤ 6
62.
-3x ≤ 18
a)
x ≤ -6
b)
x ≤ 6
c)
x ≥ 6
d)
x ≥ -6
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