Answers7th Grade Math CR Summer SchoolSolving Two-Step Inequalities

Solving Two-Step Inequalities — Unit test Answers

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1
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What is the best first step in solving ?

Question illustration
A
Add to both sides.
Option A
B
Subtract from both sides.
Option B
C
Multiply both sides by and reverse the inequality symbol.
Option C
D
Divide both sides by 10 and reverse the inequality symbol.
2
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Which inequality represents the sentence below?The difference of –3.2 and the sum of a number and 19.1 is at most 14.2.

A
Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2
Option A
B
Negative 3.2 minus x + 19.1 less-than-or-equal-to 14.2
Option B
C
Negative 3.2 minus (x + 19.1) greater-than-or-equal-to 14.2
Option C
D
Negative 3.2 minus x + 19.1 greater-than-or-equal-to 14.2
Option D
3

According to the properties of inequality, when should the inequality symbol be reversed when solving a two-step inequality in the form below?

Question illustration
A
when a is positive
B
when a is negative
C
when b is positive
D
when b is negative
4

Which statements describe the graph of on a number line? Select three options.

Question illustration
A
There is an open circle on .
Option A
B
The graph contains the point 0
C
There is a closed circle on .
Option C
D
The arrow points to the left.
E
The arrow points to the right.
5

Rico represents the inequality with the sentence “The product of –3 and the quotient of 8 and the difference of a number and 5 is at least –16.” Which describes Rico’s error?

Question illustration
A
The expression is translated incorrectly. The order of the terms in the subtraction expression should be reversed.
B
The inequality symbol is translated incorrectly. The words “at least” should be represented as greater than or equal to instead of greater than.
C
The inequality symbol is translated incorrectly. The words “at least” should be represented as less than or equal to instead of greater than.
D
The expression is translated incorrectly. The numerator and the denominator of the division expression should be reversed.
6

Allen is running a marathon. He would like to finish the race in under 5.5 hours. He has already run 3 hours. The inequality represents the situation. Which number line shows how much longer Allen can run and still meet his goal?

Question illustration
A
A number line going from 0 to 3. An open circle is at 2.5. Everything to the left of the circle is shaded.
Option A
B
A number line going from 0 to 3. A closed circle is at 2.5. Everything to the left of the circle is shaded.
Option B
C
A number line going from 0 to 3. An open circle is at 2.5. Everything to the right of the circle is shaded.
Option C
D
A number line going from 0 to 3. A closed circle is at 2.5. Everything to the right of the circle is shaded.
Option D
7

Solve the following inequality. Which graph shows the correct solution?

Question illustration
A
A number line going from negative 77 to negative 67. An open circle is at negative 72. Everything to the right of the circle is shaded.
Option A
B
A number line going from negative 77 to negative 67. An open circle is at negative 72. Everything to the left of the circle is shaded.
Option B
C
A number line going from negative 7.7 to negative 6.8. An open circle is at negative 7.2. Everything to the right of the line is shaded.
Option C
D
A number line going from negative 7.7 to negative 6.8. An open circle is at negative 7.2. Everything to the left of the line is shaded.
Option D
8

A high school coach needs to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 and needs to determine how much he can spend per pair of shorts. Write and solve an inequality to determine the maximum price for each pair of shorts. What does the solution represent?

A
The coach may spend up to $13.33 per pair of shorts.
B
The coach may spend more than $13.33 per pair of shorts.
C
The coach may spend up to $14 per pair of shorts.
D
The coach may spend more than $14 per pair of shorts.
9

Four friends share the profit of a lawn care service equally. The friends charge $45 per lawn and spend $30 of their total earnings on gasoline for the lawnmowers each week. Which inequality can be used to find m, the number of lawns they need to mow next week so that each person earns at least $275?

A
StartFraction 45 m minus 30 over 4 EndFraction greater-than-or-equal-to 275
Option A
B
StartFraction 45 m over 4 EndFraction minus 30 greater-than-or-equal-to 275
Option B
C
StartFraction 45 m minus 30 over 4 EndFraction less-than-or-equal-to 275
Option C
D
StartFraction 45 m over 4 EndFraction minus 30 less-than-or-equal-to 275
Option D
10

Yannick and Jean are playing a guessing game with integers. Yannick wrote these clues to help Jean guess the unknown integer.What is the value of the unknown integer, n?

Question illustration
A
8
B
9
C
19
D
22
11

Mercedes receives a $25 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $1.29. Write and solve an inequality to determine m, the number of songs Mercedes can purchase. What is the approximate solution to the inequality? Round to the nearest whole number.

A
m less-than-or-equal-to 19
Option A
B
m greater-than-or-equal-to 19
Option B
C
m less-than-or-equal-to 32
Option C
D
m greater-than-or-equal-to 32
Option D
12

For each babysitting job, Tamar charges $6 for bus fare plus $8 per hour. She only accepts babysitting jobs if the total charge is at least $30. What is the minimum number of hours for a babysitting job she would accept?

A
hours
Option A
B
3 hours
C
4 hours
D
hours
Option D
13

Ellen drew a graph showing the solution to an inequality. Which inequality does Ellen’s graph show the solution to?

Question illustration
A
3.25 less-than 2.5 + r
Option A
B
3.25 greater-than 2.5 + r
Option B
C
Negative 3.25 less-than negative 2.5 + r
Option C
D
Negative 3.25 greater-than negative 2.5 + r
Option D
14

Which inequalities are equivalent to ? Select three options.

Question illustration
A
n + 15 minus 15 less-than 22 minus 15
Option A
B
n + 15 less-than 22 minus 15
Option B
C
n + 15 minus 22 less-than 22 minus 22
Option C
D
n + 15 + 6 less-than 22 + 6
Option D
E
n + 15 minus 22 less-than 22
Option E
15

Solve . Which of the following must be true about the inequality and the resulting graph? Select three options.

Question illustration
A
w less-than-or-equal-to 3.6
Option A
B
The arrow points left.
C
The arrow points right.
D
There is an open circle at 3.6.
E
There is a closed circle at 3.6.

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