Understanding and Solving Linear Inequalities

The video tutorial explains how to solve and graph linear inequalities, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It provides two examples, demonstrating the process of isolating variable terms, solving the inequality, and expressing the solution graphically and in interval notation. The tutorial highlights the steps to ensure the correct representation of solutions, including the use of open and closed points on graphs and the appropriate use of parentheses and brackets in interval notation.

What must you do to the inequality symbol when you multiply or divide both sides of an inequality by a negative number?

• Multiply it by -1

• Add a negative sign

• Reverse it

• Leave it unchanged

In the first example, what is the first step to solve the inequality?

• Add 3X to both sides

• Subtract 3X from both sides

• Multiply both sides by 3

• Divide both sides by 3

In the first example, what is the result of dividing -5 by -1?

• 0

• -5

• -1

• 5

What is the solution to the first example inequality in interval notation?

• (5, ∞)

• (-∞, 5)

• [5, ∞)

• (-∞, 5]

In the second example, what operation is performed first to isolate the variable?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 5X from both sides

• Add 4 to both sides

What is the final solution for the second example inequality?

• X < 6

• X > 6

• X ≤ 6

• X ≥ 6

How is the solution to the second example represented graphically?

• Closed point on 6 with an arrow to the right

• Open point on 6 with an arrow to the left

• Closed point on 6 with an arrow to the left

• Open point on 6 with an arrow to the right

What type of bracket is used in interval notation to indicate that a number is included in the interval?

• Angle bracket

• Curly bracket

• Square bracket

• Rounded parenthesis

What is the interval notation for the solution of the second example?

• (6, ∞]

• (6, ∞)

• [6, ∞]

• [6, ∞)

What is the significance of using a rounded parenthesis in interval notation?

• It indicates the number is excluded

• It indicates the interval is finite

• It indicates the interval is infinite

• It indicates the number is included