How to set up 2 cases to solve an absolute value inequality as a compound inequality

The video tutorial demonstrates how to solve absolute value inequalities by setting up compound inequalities. It explains the process of creating two cases for the inequality and solving them step by step. The tutorial also covers graphing the solution on a number line, highlighting the importance of understanding the direction of inequalities and the values involved. The instructor provides a detailed walkthrough of each step, ensuring clarity in the process of solving and graphing absolute value inequalities.

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

• Graph the inequality on a number line

• Set up two cases for the inequality

• Add the same number to both sides

• Multiply both sides by a constant

When solving the inequality 5Z + 1 ≥ 14, what is the next step after subtracting 1 from both sides?

• Add 1 to both sides

• Subtract 5 from both sides

• Divide both sides by 5

• Multiply both sides by 5

What is the solution for Z in the inequality 5Z + 1 ≤ -15 after solving?

• Z ≥ -3

• Z ≤ -3

• Z ≤ 3

• Z ≥ 3

How do you represent the solution Z ≥ 2.6 on a number line?

• Shade all numbers to the left of 2.6

• Do not shade any numbers

• Shade all numbers to the right of 2.6

• Shade only the number 2.6

What does the filled circle on the number line represent in the context of inequalities?

• The inequality is not solved

• The inequality includes the number (greater than or equal to, less than or equal to)

• The inequality is invalid

• The inequality is strict (greater than or less than)