Solving an absolute value inequality using an and compound inequality

The video tutorial explains how to solve and graph absolute value inequalities. It begins by introducing the concept of absolute value inequalities and the need to create compound inequalities. The instructor demonstrates how to create two cases for the inequality, solve them separately, and graph the solutions on a number line. The tutorial emphasizes the importance of understanding the intersection of the inequalities and how to interpret the graph to find the solution. The video concludes with a summary of the steps involved in solving and graphing absolute value inequalities.

What is the first step in solving an absolute value inequality like |W + 6| < 2?

• Create two separate inequalities

• Divide both sides by 6

• Add 6 to both sides

• Multiply both sides by 2

When solving the inequality W + 6 < 2, what operation is performed to isolate W?

• Add 2 to both sides

• Subtract 6 from both sides

• Multiply both sides by -1

• Divide both sides by 2

How do you represent the solution of W < -4 on a number line?

• An open dot at -4 with shading to the right

• A closed dot at -4 with shading to the left

• An open dot at -4 with shading to the left

• A closed dot at -4 with shading to the right

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

• The union of the inequalities

• The solution set for both inequalities

• The absolute difference between the inequalities

• The midpoint between the inequalities

Why are open points used when graphing the solution of an inequality?

• To highlight the maximum value

• To represent a midpoint

• To show the inequality does not include the endpoint

• To indicate the inequality includes the endpoint