Introduction to Compound Inequalities Quiz

Questions and Answers

Which graph represents the compound inequality $n < -2$ or $n \geq 4$?

Line Three (open circle at -2 pointing left & closed circle at 4 pointing right) (correct)

Line Two (closed circle at -2 and open circle at 4)

Line Four (open circles at -2 and 4 with a line between them)

Line One (closed circles at -2 and 4)

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

50 ≤ e ≤ 100 (correct)

e > 100

50 < e < 100

e < 50

Which graph represents the compound inequality $-3 < n < 1$?

Line Four (open circles at -3 and 1 with a line between them) (correct)

Line Three (open circle at -3 pointing left & closed circle at 1 pointing right)

Line Two (closed circle at -3 and open circle at 1)

Line One (closed circles at -3 and 1)

Which compound inequality is represented by the graph?

-3 ≤ x < 1 Signup and view all the answers

Which compound inequality is represented by the graph?

x < -2 or x ≥ 4 Signup and view all the answers

In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. Which is another way of writing the inequality $64 < x < 68$, where $x$ represents height?

$x > 64$ and $x < 68$ Signup and view all the answers

Which set of numbers is included in the solution set of the compound inequality?

{$-7, 5, 18, 24, 32$} Signup and view all the answers

To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?

Line One (closed circles at 1.3 and 1.7, a line between them) Signup and view all the answers

To make a small vase, Elisa uses no more than 4.5 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?

c ≤ 4.5 or c ≥ 12 Signup and view all the answers

Which graph represents the compound inequality $h ≥ -5$ and $h < 2$?

Line Two (closed circle at -5 and open circle at 2, line between them) Signup and view all the answers

Study Notes

Compound Inequalities Overview

Compound inequalities consist of two separate inequalities that can be connected by "and" or "or," representing a range of solutions.
Graphs visually represent the solutions to compound inequalities, highlighting open and closed circles for inclusive or exclusive values.

Graph of Compound Inequality for n

For the inequality n < -2 or n ≥ 4, the correct graph features an open circle at -2 pointing left and a closed circle at 4 pointing right.

Earnings Inequality

Dexter's earnings must satisfy 50 ≤ e ≤ 100, indicating he earns between $50 and $100, inclusive.

Graph Representation for n

The inequality -3 < n < 1 is represented by a graph with open circles at -3 and 1, connected by a line, indicating all values between -3 and 1 are included.

Compound Inequalities from Graphs

The graph that corresponds to the compound inequality -3 ≤ x < 1 features a closed circle at -3 and an open circle at 1.
Another graph illustrates the inequality x < -2 or x ≥ 4, indicating values less than -2 or greater than or equal to 4.

Actor Height Qualification

To qualify for a play role, an actor must be taller than 64 inches but shorter than 68 inches, represented as 64 < x < 68. This can also be expressed as x > 64 and x < 68.

Solutions of Compound Inequalities

The solution set for a compound inequality includes specific values; for instance, {-7, 5, 18, 24, 32} could satisfy the terms of an inequality.

Bolt Diameter Measurement

The acceptable diameter for a bolt ranges from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm, depicted in a graph with closed circles at 1.3 cm and 1.7 cm.

Clay Usage for Vases

For clay usage, Elisa's small vase requires no more than 4.5 ounces and the large vase requires at least 12 ounces, represented by the compound inequality c ≤ 4.5 or c ≥ 12.

Compound Inequality Graph for h

The graph for the compound inequality h ≥ -5 and h < 2 includes a closed circle at -5 and an open circle at 2, indicating the boundary values.

Description

Test your understanding of compound inequalities with this quiz. It covers graph representations and inequality definitions, ensuring you grasp these concepts clearly. Perfect for students looking to solidify their knowledge in mathematics.