Solving Absolute Value Equations and Inequalities

The video tutorial covers solving absolute value equations and inequalities from both graphical and algebraic perspectives. It explains how to represent solutions on a number line using compound inequalities and separate inequalities joined by 'or' statements. The tutorial demonstrates graphing techniques to visualize solutions and discusses the algebraic process of solving these equations and inequalities, highlighting the importance of considering both positive and negative scenarios within absolute values.

What are the two perspectives used to solve absolute value equations?

• Graphical and numerical

• Graphical and algebraic

• Numerical and algebraic

• Graphical and statistical

What shape does an absolute value graph typically form?

• L-shape

• U-shape

• W-shape

• V-shape

How do you represent shading between two numbers on a number line?

• With a single inequality

• With a union of intervals

• With a compound inequality

• With a set notation

When solving absolute value equations algebraically, what do you do if the inside is negative?

• Add the negative value

• Ignore the negative value

• Square the negative value

• Do the opposite of the negative value

What is the result when solving an absolute value equation where the inside is positive?

• The absolute value becomes zero

• The absolute value is squared

• The absolute value does nothing

• The absolute value becomes negative

How do you solve an absolute value inequality followed by 'less than'?

• By writing one compound inequality

• By writing two separate inequalities

• By graphing the inequality

• By using set notation

What happens to the inequality sign when you divide by a negative number?

• It stays the same

• It becomes positive

• It switches direction

• It becomes zero

In a compound inequality, what does the 'or' statement signify?

• Both conditions must be false

• At least one condition must be true

• Both conditions must be true

• Neither condition must be true

What is the graphical representation of an absolute value inequality followed by 'greater than'?

• A horizontal line

• A single point

• A single region

• Two separate regions

When solving absolute value inequalities, what must you consider if the inside is negative?

• Ignore the negative value

• Square the negative value

• Add the negative value

• Do the opposite of the negative value