Understanding and Solving Inequalities

The video tutorial explains how to solve and graph inequalities with the variable on the right side. It demonstrates the process of isolating the variable, reversing the inequality for easier graphing, and expressing the solution using interval notation. Two examples are provided, showing how to handle inequalities with different symbols and how to graph them on a number line. The tutorial emphasizes understanding the direction of the inequality symbol and the use of open or closed points on the graph, as well as the appropriate use of parentheses or brackets in interval notation.

What is the first step in solving an inequality with the variable on the right side?

• Multiply both sides by the same number

• Subtract the same number from both sides

• Divide both sides by the same number

• Add the same number to both sides

When solving the inequality -5 > x, what is the equivalent form?

• x > -5

• x < -5

• -5 < x

• x = -5

How is the graph of x < -5 represented?

• A closed point on -5 with a line to the right

• An open point on -5 with a line to the right

• A closed point on -5 with a line to the left

• An open point on -5 with a line to the left

What type of bracket is used in interval notation for a value that is not included?

• Angle bracket

• Rounded parenthesis

• Curly bracket

• Square bracket

What operation is performed to isolate x in the inequality 9 ≤ x + 4?

• Divide both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply both sides by 4

What is the equivalent form of the inequality 5 ≤ x?

• x < 5

• x > 5

• x ≥ 5

• x ≤ 5

How is the graph of x ≥ 5 represented?

• A closed point on 5 with a line to the right

• An open point on 5 with a line to the right

• A closed point on 5 with a line to the left

• An open point on 5 with a line to the left

What type of bracket is used in interval notation for a value that is included?

• Angle bracket

• Square bracket

• Curly bracket

• Rounded parenthesis

In interval notation, what symbol is used to represent infinity?

• ∞

• -∞

• 0

• 1

What is the interval notation for the solution x ≥ 5?

• [5, ∞)

• (5, ∞]

• (5, ∞)

• [5, ∞]