Understanding Absolute Value Inequalities

This video tutorial explains how to solve an absolute value inequality by isolating the absolute value, setting up compound inequalities, solving them, and expressing the solution as a graph and using interval notation. The process involves undoing operations to isolate the absolute value, creating two inequalities connected by 'or', solving them, and graphing the solution. The final solution is expressed in interval notation, highlighting the union of the intervals.

What is the first step in solving an absolute value inequality?

• Using interval notation

• Setting up a compound inequality

• Isolating the absolute value

• Graphing the inequality

When isolating the absolute value, what operation should be performed first?

• Division

• Multiplication

• Addition

• Subtraction

After isolating the absolute value, what is the next step in solving the inequality?

• Graphing the solution

• Setting up a compound inequality

• Using interval notation

• Checking the solution

How do you set up the second inequality when dealing with an absolute value inequality?

• Reverse the inequality symbol and change the sign of the number

• Keep the inequality symbol the same

• Add the same number to both sides

• Multiply both sides by -1

What does the graph of the solution to an absolute value inequality represent?

• The union of intervals

• A closed interval

• A single point

• The intersection of intervals

In graphing the solution, what does an open point on the number line indicate?

• The interval is infinite

• The interval is closed

• The number is not included in the interval

• The number is included in the interval

What symbol is often used to represent the union of two intervals?

• →

• ∞

• ∪

• ∩

How is the interval from 2 to infinity expressed in interval notation?

• [2, ∞)

• [2, ∞]

• (2, ∞]

• (2, ∞)

What does a rounded parenthesis in interval notation signify?

• The endpoint is included

• The endpoint is excluded

• The interval is closed

• The interval is finite

What is the purpose of using interval notation in expressing solutions?

• To graph the solution

• To express the solution in a concise form

• To solve the inequality

• To check the solution