AnswersAlgebra 1Introduction to Compound Inequalities

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To make a small vase, Elisa uses no more than 4 point 5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c , that Elisa uses to make one vase of either size?

A
4 point 5 is less than or equal to c comma c is less than or equal to 12
B
4 point 5 is less than c comma c is less than 12
C
c is less than or equal to 4 point 5 or c is greater than or equal to 12
D
c is less than 4 point 5 or c is greater than 12
3

For one photography session, Dexter earns no less than 50 dollars , but no more than 100 dollars Which inequality can be used to represent his earnings, e ?

A
50 is less than e comma e is less than 100
B
50 is less than or equal to e comma e is less than or equal to 100
C
e is greater than 50 or e is less than 100
D
e is greater than or equal to 50 or e is less than or equal to 100
4

Which graph represents the compound inequality? h is greater than or equal to negative 5 and h is less than 2

A
Image with description A number line labeled from negative 6 to 4 in increments of 1 from left to right. An open circle is at negative 5 and a solid circle is at 2 with a line segment connecting them.
B
Image with description A number line labeled from negative 6 to 4 in increments of 1 from left to right. A solid circle is at negative 5 and an open circle is at 2 with a line segment connecting them.
C
Image with description A number line labeled from negative 6 to 4 in increments of 1 from left to right. A solid circle is at negative 5 with an arrow pointing to the left. An open circle is at 2 with an arrow pointing to the right.
D
Image with description A number line labeled from negative 6 to 4 in increments of 1 from left to right. An open circle is at negative 5 with an arrow pointing to the left. A solid circle is at 2 with an arrow pointing to the right.
5

Which compound inequality is represented by the graph? Open image in full-screen view

A
negative 3 is less than or equal to x comma x is less than 1
B
negative 3 is less than x comma x is less than or equal to 1
C
x is less than or equal to negative 3 or x is greater than 1
D
x is less than negative 3 or x is greater than or equal to 1
6

Which compound inequality is represented by the graph? Open image in full-screen view

A
x is less than or equal to negative 2 or x is greater than 4
B
negative 2 is less than x comma x is less than or equal to 4
C
negative 2 is less than or equal to x comma x is less than 4
D
x is less than negative 2 or x is greater than or equal to 4
7

To support a shelf, the diameter of a bolt can measure anywhere from 0 point 2 cm less than 1 point 5 cm to 0 point 2 cm greater than 1 point 5 cm. Which graph represents the possible measures of the diameter of the bolt?

A
Image with description A number line labeled from 1 to 2 in increments of 0 point 2. There is an open dot at 1 point 3 and another open dot at 1 point 7. Both the dots are connected.
B
Image with description A number line is labeled from 1 to 2 in increments of 0.1. The line is shaded from 1.3 to 1.7 with filled circles at 1.3 and 1.7.
C
Image with description A number line labeled from 1 to 2 in increments of 0 point 2. An open dot at 1 point 3 from which a ray extends to the left, and another open dot at 1 point 7 from which a ray extends to the right.
D
Image with description A number line labeled from 1 to 2 in increments of 0 point 2. A closed dot at 1 point 3 from which a ray extends to the left, and a closed dot at 1 point 7 from which a ray extends to the right.
8

The weight of a box of cereal can vary by 1 fourth of an ounce and still be sold as a full box. Each box is supposed to contain 18 ounces of cereal. Which graph represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes?

A
Image with description A number line is labeled from 17.5 to 18.5 in increments of 0.125. The line is shaded from 17.75 to 18.25 with closed circles at 17.75 and 18.25.
B
Image with description A number line labeled from 17 point 5 to 18 point 5 in increments of 0 point 25. There is a closed dot at 17 point 7 5, a ray from the point extends towards the left. Another closed dot at 18 point 2 5, a ray from the point extends towards the right.
C
Image with description A number line labeled from 17 point 5 to 18 point 5 in increments of 0 point 25. There is an open dot at 17 point 7 5, a ray from the point extends towards the left. Another open dot at 18 point 2 5, a ray from the point extends towards the right.
D
Image with description A number line is labeled from 17.5 to 18.5 in increments of 0.125. The line is shaded from 17.75 to 18.25 with open circles at 17.75 and 18.25.
9

Which set of numbers is included in the solution set of the compound inequality? Open image in full-screen view

A
start set negative 9 comma 7 comma 15 comma 22 comma 26 end set
B
start set 18 comma 19 comma 20 comma 21 comma 22 end set
C
start set 16 comma 17 comma 22 comma 23 comma 24 end set
D
start set negative 7 comma 5 comma 18 comma 24 comma 32 end set
10

A political polling agency predicts candidate A will win an election with 54 percent of the votes. Their poll has a margin of error of 4 percent both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x , for candidate A?

A
52 is less than or equal to x comma x is less than or equal to 56
B
x is greater than or equal to 52 or x is less than or equal to 56
C
x is greater than or equal to 50 or x is less than or equal to 58
D
50 is less than or equal to x comma x is less than or equal to 58

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