Understanding Inequalities and Interval Notation

The video tutorial explains how to solve and graph inequalities using interval notation. It covers two examples: solving X + 5 > 3 and X - 7 ≤ -3. For each example, the process of isolating X is demonstrated, followed by graphing the solution on a number line. The video also explains how to use interval notation to represent the solutions, including the use of open and closed points and the concept of approaching infinity.

What is the first step in solving an inequality like X + 5 > 3?

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 5

• Divide both sides by 5

After solving X + 5 > 3, what is the solution for X?

• X < -2

• X < 2

• X > -2

• X > 2

How do you represent that a number is not included in an interval on a graph?

• Use a closed point

• Use a square bracket

• Use an open point

• Use a dashed line

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

• Square bracket

• Curly brace

• Angle bracket

• Rounded parenthesis

In the inequality X - 7 <= -3, what operation is used to isolate X?

• Multiply both sides by 7

• Add 7 to both sides

• Divide both sides by 7

• Subtract 7 from both sides

What is the solution for X in the inequality X - 7 <= -3?

• X > 4

• X < 4

• X >= 4

• X <= 4

How is the number 4 represented on the graph for the inequality X - 7 <= -3?

• With an open point

• With a closed point

• With a square bracket

• With a dashed line

In interval notation, how is the interval for X - 7 <= -3 written?

• [4, ∞]

• (-∞, 4)

• [4, ∞)

• (-∞, 4]

What type of parenthesis is used for positive and negative infinity in interval notation?

• Square bracket

• Curly brace

• Rounded parenthesis

• Angle bracket

What does a closed point on a graph indicate about a number in an interval?

• The number is not included

• The number is included

• The number is an endpoint

• The number is a midpoint