AnswersV Algebra 2 S1Real Numbers

Inequalities Answers

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1
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Find the student’s error in solving the following inequality.31 < –5x + 6 25 < –5x –5 < x

A
The student should have added 6 to both sides instead of subtracting it.
B
The student divided 25/–5 incorrectly.
C
The student should have switched the direction of the inequality sign to get –5> x for a final answer.
2
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Find the student’s error in solving the following inequality.2 x > –5/3

A
The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.
B
The student divided 6/–3 incorrectly.
C
The student should not have switched the direction of the sign in the final step.
3

Which graph represents the solution set of the compound inequality ?

Question illustration
A
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7.
Option A
B
A number line goes from negative 10 to positive 10. A closed circle appears at negative 7 and positive 1. The number line is shaded from negative 7 to positive 1.
Option B
C
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1. The number line is shaded from negative 1 toward negative 10.
Option C
D
A number line goes from negative 10 to positive 10. A closed circle appears on positive 7. The number line is shaded from positive 7 toward positive 10.
Option D
4

Which is the solution set of the inequality

Question illustration
A
y greater-than nine-fifths
Option A
B
y less-than nine-fifths
Option B
C
y less-than 3
Option C
D
y greater-than 3
Option D
5

Which values of x satisfy the inequality

Question illustration
A
x greater-than-or-equal-to 5
Option A
B
x less-than-or-equal-to 5
Option B
C
x less-than-or-equal-to 8
Option C
D
x greater-than-or-equal-to 8
Option D
6

Which graph shows the solution to the inequality

Question illustration
A
A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through negative 10.
Option A
B
A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.
Option B
C
A number lines goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through negative 10.
Option C
D
A number line goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through positive 10.
Option D
7

Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?

A
10 weeks
B
12 weeks
C
15 weeks
D
20 weeks
8

Which graph shows the solution set of the inequality

Question illustration
A
A number line goes from negative 10 to positive 10. A solid circle appears at 0. The number line is shaded from 0 toward positive 10.
Option A
B
A number line goes from negative 10 to positive 10. An open circle appears at 0. The number line is shaded from 0 toward positive 10.
Option B
C
A number line goes from negative 10 to positive 10. A closed circle appears at positive 1. The number line is shaded from positive 1 toward negative 10.
Option C
D
A number line goes from negative 10 to positive 10. An open circle appears at positive 1. The number line is shaded from positive 1 toward negative 10.
Option D
9

Six times a number is greater than 20 more than that number. What are the possible values of that number?

A
n less-than 4
Option A
B
n greater-than 4
Option B
C
n greater-than StartFraction 20 Over 7 EndFraction
Option C
D
n less-than StartFraction 20 Over 7 EndFraction
Option D
10

Which graph represents the solution set of the inequality

Question illustration
A
A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9.
Option A
B
A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9.
Option B
C
A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9.
Option C
D
A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.
Option D
11

A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?

A
m less-than-or-equal-to 17
Option A
B
m greater-than-or-equal-to 17
Option B
C
m less-than-or-equal-to 20.3
Option C
D
m greater-than-or-equal-to 20.3
Option D
12

Which represents the solution set of

Question illustration
A
x less-than 12
Option A
B
x greater-than 12
Option B
C
x less-than 16
Option C
D
x greater-than 16
Option D
13

Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of the summer. He withdraws $28 each week for food. Which inequality represents w, the number of weeks Manuel can withdraw money while not dropping below a $300 balance?

A
28 minus 600 w less-than-or-equal-to 300
Option A
B
28 minus 600 w greater-than-or-equal-to 300
Option B
C
600 minus 28 w less-than-or-equal-to 300
Option C
D
600 minus 28 w less-than-or-equal-to 300
Option D
14

Which represents the solution set of the inequality

Question illustration
A
x less-than-or-equal-to twelve-fifths
Option A
B
x greater-than-or-equal-to twelve-fifths
Option B
C
x greater-than-or-equal-to 6
Option C
D
x less-than-or-equal-to 6
Option D
15

Grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee. If h represents the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?

A
h less-than 2
Option A
B
h greater-than 2
Option B
C
h less-than 5
Option C
D
h greater-than 5
Option D
16

Serena makes $9 per hour cutting lawns. Each day, she earns about $15 in tips. If Serena made no less than $110 on Monday, which inequality represents h, the number of hours she worked on Monday?

A
15 h + 9 less-than-or-equal-to 110
Option A
B
15 h + 9 greater-than-or-equal-to 110
Option B
C
9 h + 15 greater-than-or-equal-to 110
Option C
D
9 h + 15 less-than 110
Option D

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