Understanding Inequalities and Interval Notation

The video tutorial explains how to solve inequalities by distributing terms, combining like terms, and isolating the variable x. It emphasizes the importance of reversing the inequality symbol when multiplying or dividing by a negative number. The tutorial also covers graphing solutions using open points and line segments, and explains how to express solutions in interval notation, including the use of infinity symbols.

What must you remember to do when multiplying or dividing both sides of an inequality by a negative number?

• Subtract the same number from both sides

• Multiply by zero

• Add the same number to both sides

• Reverse the inequality symbol

What is the result of distributing 4 in the expression 4(9x - 14)?

• 36x - 56

• -36x + 56

• 36x + 56

• -36x - 56

After combining like terms, what is the simplified form of the inequality 24x > 60 - 36x?

• 60x < 60

• 24x < 60

• 24x > 36

• 60x > 60

What is the inequality solution for x if 60x > 60?

• x < 1

• x ≤ 1

• x > 1

• x = 1

How do you represent that the endpoint is not included in a graph on a number line?

• Use a closed point

• Use a shaded region

• Use a dashed line

• Use an open point

Which tool is used to graph an open point on a number line?

• Line Segment tool

• Closed Dot tool

• Arrow tool

• Open Dot tool

What symbol is used in interval notation to indicate that an endpoint is not included?

• Angle bracket

• Parenthesis

• Curly brace

• Square bracket

In interval notation, how is positive infinity represented?

• With an angle bracket

• With a parenthesis

• With a curly brace

• With a square bracket

What is the interval notation for x > 1?

• [1, ∞)

• (1, ∞]

• [1, ∞]

• (1, ∞)

What does an open parenthesis in interval notation signify?

• The endpoint is not included

• The interval is closed

• The endpoint is included

• The interval is infinite