Understanding Inequalities and Interval Notation

The video tutorial explains how to plot inequalities on a number line and express them using interval notation. It covers two examples: one where X is greater than -3 and another where X is less than or equal to 2. The tutorial highlights the use of open and closed points to indicate whether a number is included in the interval and explains the use of parentheses and brackets in interval notation.

What is the first step in plotting inequalities on a number line?

• Start with positive infinity.

• Draw a closed point on the number line.

• Identify the inequality and its direction.

• Use a square bracket for all intervals.

How do you represent the inequality X > -3 on a number line?

• Draw a closed point on -3 and an arrow to the left.

• Draw an open point on -3 and an arrow to the right.

• Draw an open point on -3 and an arrow to the left.

• Draw a closed point on -3 and an arrow to the right.

What symbol is used in interval notation to indicate that a number is not included in the interval?

• Curly brace

• Open point

• Parenthesis

• Square bracket

In interval notation, what is always used to the right of positive infinity?

• Square bracket

• Curly brace

• Parenthesis

• Open point

Which of the following is true about the use of brackets in interval notation?

• Parentheses are used for both included and not included numbers.

• Square brackets are used for numbers included in the interval.

• Parentheses are used for numbers included in the interval.

• Square brackets are used for numbers not included in the interval.

How is the inequality X ≤ 2 represented on a number line?

• Closed point on 2 with an arrow to the right

• Open point on 2 with an arrow to the left

• Closed point on 2 with an arrow to the left

• Open point on 2 with an arrow to the right

What is the interval notation for X ≤ 2?

• (-∞, 2]

• (-∞, 2)

• [2, ∞)

• (2, ∞)

What does a closed point on a number line indicate?

• The interval is finite.

• The interval is infinite.

• The number is not part of the interval.

• The number is part of the interval.