Exploring Absolute Value Equations and Inequalities

The video tutorial covers the setup and solving of absolute value equations and inequalities. It begins with an introduction to the basic structure of these equations, followed by example problems to illustrate the concepts. The tutorial then applies these equations to word problems, demonstrating how to find acceptable ranges for variables. Finally, it explores graphical representations of absolute value equations, explaining how to interpret and write equations based on graphs.

What is the basic structure of an absolute value equation?

• Absolute value of the sum of actual and ideal amounts

• Absolute value of the difference between actual and ideal amounts

• Absolute value of the product of actual and ideal amounts

• Absolute value of the quotient of actual and ideal amounts

In the example 'all numbers less than three units from zero', what is the ideal amount?

• 6

• 0

• x

• 3

For the word problem involving the piston diameter, what is the variance?

• 0.008 millimeters

• 90 millimeters

• 0.05 millimeters

• 33.86 millimeters

In the word problem about the model airplane engine, what is the ideal weight?

• 33.91 ounces

• 33.81 ounces

• 33.86 ounces

• 0.05 ounces

When writing absolute value equations from graphs, what does it mean if there are no shading and no lines, just two dots?

• It represents a function

• It represents an inequality

• It represents a system of equations

• It represents an equation

In the graph example with points at -3 and 3, what is the variance?

• 0

• 3

• 1

• 6

In the graph example with points at -4 and 2, what is the ideal amount?

• -1

• 0

• -4

• 2

For the graph example with open circles, what type of statement is it?

• And statement

• Or statement

• Function

• Equation

In the graph example with points at -2 and 6, what is the variance?

• 4

• 6

• 2

• 8

For the graph example with closed circles, what type of statement is it?

• Function

• Equation

• Or statement

• And statement