Exploring Inequalities and Absolute Value Equations

The video tutorial covers linear inequalities, absolute value equations, and inequalities. It begins with an introduction to linear inequalities, explaining how to solve and graph them. The tutorial then moves on to compound inequalities, detailing how to determine solution sets and graph them. The focus shifts to absolute value equations, outlining steps to solve them with examples. Finally, the video addresses absolute value inequalities, demonstrating how to solve and graph these inequalities.

What is the first step in solving a linear inequality like 2x - 4 > 10?

• Divide both sides by 2

• Multiply both sides by 2

• Add 4 to both sides

• Subtract 4 from both sides

When graphing the solution x > 7 on a number line, what type of circle is used at 7?

• No circle

• Closed circle

• Open circle

• Shaded circle

What must you do to the inequality sign when you multiply or divide both sides by a negative number?

• Leave it unchanged

• Subtract 1 from it

• Flip it

• Add 1 to it

In a compound inequality, if the signs are going in opposite directions, what should you do?

• Combine them

• Leave them as separate inequalities

• Flip one of the signs

• Add the inequalities together

What does absolute value represent?

• The reciprocal of a number

• The distance from zero

• The negative value of a number

• The square of a number

What is the first step in solving an absolute value equation like |3x - 6| - 2 = 4?

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by 3

• Multiply both sides by 3

When solving absolute value equations, why do we write two equations?

• To eliminate the absolute value bars

• To account for both positive and negative solutions

• To check for errors

• To simplify the equation

What should you never do when dealing with absolute value equations?

• Add to both sides

• Subtract from both sides

• Distribute within the absolute value bars

• Divide both sides

When solving absolute value inequalities, what happens to the inequality sign when you flip the sign of the equation?

• It is removed

• It becomes an equal sign

• It flips as well

• It stays the same

In absolute value inequalities, what does a 'greater than' inequality indicate about the solution set?

• It is an 'and' solution

• It is an 'or' solution

• It is a 'not' solution

• It is a 'both' solution