3 Absolute Inequalities You Have To Know to Pass

This video tutorial explores solving and graphing absolute value inequalities through three examples. It covers basic to intermediate problems, focusing on isolating absolute values and understanding compound inequalities. The tutorial demonstrates solving inequalities with multiplication, operations inside and outside absolute values, and more complex scenarios. It emphasizes the importance of considering both positive and negative cases and provides guidance on graphing solutions and writing interval notation.

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

• Graph the inequality

• Add a constant to both sides

• Isolate the absolute value

• Multiply both sides by a constant

When solving an absolute value inequality where the absolute value is greater than a number, what type of inequality is formed?

• Compound inequality

• OR inequality

• AND inequality

• Simple inequality

In the context of absolute value inequalities, what does it mean to 'flip the sign'?

• Reverse the direction of the inequality symbol

• Switch the terms on both sides

• Add a constant to both sides

• Change the inequality to an equation

How do you determine the intersection of solutions in an AND inequality?

• Add the solutions together

• Graph the solutions separately

• Find where at least one condition is true

• Find where both conditions are true

What is the purpose of using interval notation in graphing inequalities?

• To eliminate the absolute value

• To convert the inequality to an equation

• To express the range of solutions

• To simplify the inequality

In an advanced example, what is the first step to isolate the absolute value?

• Divide both sides by a constant

• Subtract a constant from both sides

• Multiply both sides by a constant

• Add a constant to both sides

When graphing the solution of an OR inequality, what is important to remember?

• Only one condition needs to be true

• Both conditions must be true

• The solution is always a single point

• The solution is always an empty set

What does a closed circle on a graph indicate in the context of inequalities?

• The inequality is undefined

• The value is excluded from the solution

• The inequality is an equation

• The value is included in the solution

How do you express a solution that extends to infinity in interval notation?

• Use brackets

• Use a semicolon

• Use parentheses

• Use curly braces

What is the significance of using a union in interval notation?

• To express an undefined interval

• To combine overlapping intervals

• To separate distinct intervals

• To indicate a single interval