Understanding Compound Inequalities

The video tutorial explains how to graph compound inequalities and express them using interval notation. It distinguishes between 'and' and 'or' compound inequalities, showing how 'and' requires the intersection of solutions, while 'or' requires the union. The tutorial provides step-by-step instructions for graphing inequalities on a number line and converting them into interval notation. Two examples are given: one where the solution is a union of two intervals and another where the solution covers all real numbers.

What is the solution of a compound inequality when two inequalities are joined by 'and'?

• The union of the solutions

• The intersection of the solutions

• The difference of the solutions

• The sum of the solutions

In a compound inequality joined by 'or', when is the solution true?

• When both inequalities are false

• When at least one inequality is true

• When both inequalities are true

• When neither inequality is true

How do you represent x ≤ -4 on a number line?

• Open circle on -4, arrow to the right

• Closed circle on -4, arrow to the left

• Open circle on -4, arrow to the left

• Closed circle on -4, arrow to the right

What type of circle is used on the number line for x > 3?

• Half-open circle

• No circle

• Open circle

• Closed circle

How is the interval notation for x ≤ -4 expressed?

• (-∞, -4)

• (-∞, -4]

• (-4, ∞)

• [-4, ∞)

What is the interval notation for the union of x ≤ -4 or x > 3?

• (-∞, -4) ∪ (3, ∞)

• (-∞, -4] ∪ (3, ∞)

• (-∞, -4] ∪ [3, ∞)

• (-∞, -4) ∪ [3, ∞)

How do you represent x > -2 on a number line?

• Closed circle on -2, arrow to the right

• Open circle on -2, arrow to the left

• Closed circle on -2, arrow to the left

• Open circle on -2, arrow to the right

What type of circle is used on the number line for x ≤ 6?

• Closed circle

• No circle

• Half-open circle

• Open circle

What is the interval notation for all real numbers?

• [0, ∞)

• (-∞, ∞)

• (-∞, 0]

• (-∞, ∞]

What does the union of x > -2 or x ≤ 6 represent on a number line?

• Only positive numbers

• Only negative numbers

• All real numbers

• No numbers