Answers4413VA ALGEBRA 3 SEM ASolving Compound Inequalities

Solving Compound Inequalities — Unit test Answers

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Ava solved the compound inequality + 7 < –1 or 2x – 1 ≥ 9 for all possible values of x. Which graph represents the solution set?

Question illustration
A
A number line with a point at negative 32 with a bold line pointing to the left and an open circle at 5 with a bold line pointing to the right.
Option A
B
A number line with an open circle at negative 32 with a bold line pointing to the left and a point at 5 with a bold line pointing to the right.
Option B
C
A number line with a point at negative 32 with a bold line pointing to the right stopping at the open circle at 5.
Option C
D
A number line with an open circle at negative 32 with a bold line pointing to the right stopping at the point 5.
Option D
2
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Which compound inequality has no solution?

A
x ≤ –2 and 2x ≥ 6
B
x ≤ –1 and 5x ≤ 5
C
x ≤ –1 and 3x ≥ –3
D
x ≤ –2 and 4x ≤ –8
3

Which best describes the solution set for the inequality below?3x + 7 ≤ 4x – 8 or –2x + 3 ≥ 1

A
x ≤ 1 or x ≥ 15
B
x ≥ 1 or x ≤ 15
C
x ≥ 1
D
x ≤ 15
4

Phyllis solved the compound inequality 16 ≤ 2(3x – 1) < 28. She began by first breaking the inequality into two separate inequalities, then she correctly solved each for x.Which graph represents her solution?

A
A number line with a point at 3 with a bold line pointing to the right stopping at the open circle at 5.
Option A
B
A number line with an open circle at 3 with a bold line pointing to the right stopping at the point 5.
Option B
C
A number line with a point at 3 with a bold line pointing to the left and an open circle at 5 with a bold line pointing to the right.
Option C
D
A number line with an open circle at 3 with a bold line pointing to the left and a point at 5 with a bold line pointing to the right.
Option D
5

The cost of one pound of bananas is greater than $0.41 and less than $0.50. Sarah pays $3.40 for x pounds of bananas. Which inequality represents the range of possible pounds purchased?

A
0.41 < < 0.50
Option A
B
0.41 < < 0.50
Option B
C
0.41 < 3.40x < 0.50
D
0.41 < 3.40 + x < 0.50
6

Which compound inequality has no solution?

A
x > 2 and 3x ≤ 9
B
x > 1 and 2x ≤ –2
C
x > –1 and 4x ≥ –8
D
x > –2 and 5x ≥ 15
7

Which is the best interpretation of the solution set for the compound inequality?3(2x + 1) > 21 or 4x + 3 < 3x + 7

A
no solution
B
3 < x < 4
C
x 4
D
all real numbers
8

Which graph represents the solution to the compound inequality?–6 < 3x – 12 ≤ 9

A
A number line with an open circle at 2 with a bold line pointing to the left. A point at 7 with a bold line pointing to the right.
Option A
B
A number line with an open circle at 2 with a bold line pointing to the right ending at the point at 7.
Option B
C
A number line with an open circle at negative 6 with a bold line pointing to the left. A point at 9 with a bold line pointing to the right.
Option C
D
A number line with an open circle at negative 6 with a bold line pointing to the right ending at the point at 9.
Option D
9

Solve for x.0 ≤ 3x – 6 ≤ 18

A
0 ≤ x ≤ 8
B
2 ≤ x ≤ 8
C
x ≤ 0 or x ≥ 8
D
x ≤ 2 or x ≥ 8
10

For a wrestler to qualify in his weight class, he needs to weigh more than 165 pounds but less than or equal to 185 pounds. He currenty weighs 189 pounds and is losing 0.5 of a pound per week.

A
165 ≤ 189 – 0.5w < 185
B
165 < 189 – 0.5w ≤ 185
C
165 > 189 – 0.5w or 185 ≤ 189 – 0.5w
D
165 ≥ 189 – 0.5w or 185 < 189 – 0.5w
11

Mrs. Sawyer estimates that a quiz will take students no fewer than 11 minutes but no more than 41 minutes to complete. She allots 1 minute for passing out the papers and instructions and then students will complete a 20-question quiz. Which compound inequality represents x, the average amount of time a student spends on each question?

A
1 + 20x > 11 or 1 + 20x < 41
B
11 < 1 + 20x < 41
C
11 ≤ 1 + 20x ≤ 41
D
1 + 20x ≥ 11 or 1 + 20x ≤ 41
12

Solve for x.5x – 10 > 20 or 5x – 10 ≤ –15

A
–5 ≤ x < 6
B
–1 ≤ x < 6
C
x ≤ –5 or x > 6
D
x ≤ –1 or x > 6
13

Which is the best interpretation of the solution set for the compound inequality?x – 1 < 2x + 4 or 3(x + 1) < 11

Question illustration
A
no solution
B
x > –10
C
x < 4
D
all real numbers
14

A sugar solution currently measures 250 degrees Fahrenheit. The temperature of the solution increases 5 degrees per minute. The sugar solution will caramelize at temperatures greater than 310 and less than 338 degrees Fahrenheit. Which inequality can be used to find x, the number of minutes it will take for the solution to begin caramelizing?

A
310 < 250 + 5x < 338
B
310 < 250 + 5x < 338
C
310 < 5(x + 250) < 338
D
310 < 5(x + 250) < 338
15

Which graph represents the solution set for the compound inequality below?x+ 10 ≥ 7x – 10 ≥ 7

Question illustration
A
A number line with a point at 9 with a bold line pointing to the left. A point at 17 with a bold line pointing to the right.
Option A
B
A number line with a point at 9 with a bold line pointing to the right.
Option B
C
A number line with a point at 1 with a bold line pointing to the left. A point at 17 with a bold line pointing to the right.
Option C
D
A number line with a point at 1 with a bold line pointing to the right.
Option D
16

Which values are in the solution set of the compound inequality –8 < 3x + 7 ≤ 10? Select three options.–15–5–301

A
–15
B
–5
C
–3
D
0
E
1

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