Solve and graph an absolute value inequality

The video tutorial explains how to solve and graph inequalities involving absolute values. It begins by discussing the concept of absolute value and its implications for inequalities, emphasizing the need for two solutions. The instructor demonstrates how to isolate the absolute value and set up two scenarios to solve the inequality. The process of solving the inequality and graphing it on a number line is shown, including the use of open circles for less than and greater than signs. Finally, the video covers compound inequalities and how to graph them to find the solution set.

What is the first step when dealing with an absolute value inequality?

• Combine like terms

• Add a constant to both sides

• Isolate the absolute value sign

• Multiply both sides by 2

When solving an absolute value inequality, why do we set up two different situations?

• To eliminate fractions

• To simplify the equation

• To account for both positive and negative solutions

• To check for errors

What must you remember to do when you multiply or divide by a negative number in an inequality?

• Add 1 to both sides

• Flip the inequality sign

• Subtract 1 from both sides

• Keep the inequality sign the same

How is an open circle used on a number line when graphing inequalities?

• To show the endpoint is not included

• To indicate a solution is included

• To represent a closed interval

• To mark the midpoint

What does the intersection of two inequalities on a number line represent?

• The range of all real numbers

• The midpoint of the number line

• The solution set for the compound inequality

• The union of all possible solutions