Exploring Interval Notation and Compound Inequalities

This video tutorial covers interval notation and compound inequalities. It explains how to write inequalities in interval notation, convert between graphs and inequalities, and solve compound inequalities. The tutorial includes examples of both 'and' and 'or' compound inequalities, demonstrating how to graph and write interval notation for each. The video emphasizes the importance of understanding the symbols used in interval notation and provides step-by-step solutions to various inequality problems.

What symbol is used in interval notation to indicate that an endpoint is not included?

• Infinity

• Parenthesis

• Bracket

• Comma

In interval notation, what does a bracket signify?

• The interval is undefined

• The interval's endpoint is included

• The interval's endpoint is not included

• The interval continues forever

Given a graph with an open circle at 2 and shading to the right, what is the correct inequality?

• x < 2

• x ≤ 2

• x ≥ 2

• x > 2

For a graph with a closed circle at 4 and shading to the left, what is the interval notation?

• (-∞, 4]

• (4, ∞)

• (-∞, 4)

• [4, ∞)

What is a compound inequality?

• An inequality with no solution

• An inequality with two distinct parts joined by 'and' or 'or'

• An inequality that only uses brackets

• An inequality that only uses parentheses

In a compound inequality, what does the 'and' statement imply?

• The solution must satisfy both inequalities simultaneously

• The solution must satisfy at least one inequality

• The solution is always positive

• The solution is always negative

How do you solve the compound inequality: -3 ≤ x - 4 < -1?

• Subtract 4 from all parts

• Multiply all parts by 4

• Add 4 to all parts

• Divide all parts by 4

When solving a compound inequality, what must you remember to do when dividing by a negative number?

• Subtract the negative number from all parts

• Keep the inequality signs the same

• Flip the inequality signs

• Add the negative number to all parts

What is the interval notation for the solution to the inequality: x > 10 or x < 5?

• (10, ∞) ∪ (-∞, 5]

• (10, ∞) ∪ (-∞, 5)

• [10, ∞) ∪ (-∞, 5]

• [10, ∞) ∪ (-∞, 5]

In the inequality -3x + 1 ≤ -29 or 2x - 3 < 7, what is the solution for x?

• x ≥ 10 or x < 5

• x ≤ 10 or x > 5

• x ≥ -10 or x < -5

• x ≤ -10 or x > -5