Understanding Absolute Value Equations

The video tutorial covers solving absolute value equations both algebraically and graphically. It begins with a definition of absolute value, explaining it as the distance from zero on a number line, which is always positive. The tutorial then discusses the principles of absolute value equations, including cases with positive, zero, and negative values. It provides a step-by-step guide to solving these equations algebraically, emphasizing the importance of isolating the absolute value and setting up two equations. The video also demonstrates how to solve these equations graphically by plotting the equations and finding points of intersection.

What is the absolute value of -3?

• 3

• 0

• -3

• 6

Which of the following is true about the absolute value of a number?

• It can be negative.

• It represents the distance from zero.

• It is the same as the number itself.

• It is always zero.

If the absolute value of X equals a positive number C, what are the possible solutions for X?

• X = 0

• X = C only

• X = -C only

• X = C or X = -C

What is the first step in solving an absolute value equation algebraically?

• Isolate the absolute value

• Graph the equation

• Add a constant to both sides

• Check the solutions

What happens if an absolute value equation equals a negative number?

• It has one solution

• It has two solutions

• It has infinite solutions

• It has no solution

In the equation |2X + 3| = 9, what are the two equations you need to solve?

• 2X = 9 and 2X = -9

• 2X + 3 = 9 and 2X = 9

• 2X + 3 = 0 and 2X + 3 = 9

• 2X + 3 = 9 and 2X + 3 = -9

Why is it important to check your solutions when solving absolute value equations?

• To ensure the solutions are positive

• To verify the solutions satisfy the original equation

• To find more solutions

• To simplify the equation further

What is the first step in solving absolute value equations graphically?

• Calculate the slope

• Graph the right side of the equation

• Graph the left side of the equation

• Find the x-intercepts

When graphing absolute value equations, what do the x-coordinates of the points of intersection represent?

• The y-intercepts

• The solutions to the equation

• The midpoint of the graph

• The slope of the line

What should you do if the standard window does not show the horizontal line when graphing?

• Change the x-minimum

• Change the y-maximum

• Change the y-minimum

• Change the x-maximum