Solving and Graphing Compound Inequalities

The video tutorial explains compound inequalities, focusing on two types: 'and' and 'or'. It details methods to solve 'and' inequalities using the 'three-headed monster' method and graphing on a number line. For 'or' inequalities, it covers solving and graphing on both a number line and a coordinate plane. The tutorial emphasizes understanding boundary points and shading regions to represent solutions.

What are the two types of compound inequalities?

• Linear and quadratic inequalities

• Simple and complex inequalities

• And and or inequalities

• Single and double inequalities

In the 'and' type compound inequality, what is the first step in the three-headed monster method?

• Divide all three expressions by 2

• Multiply all three expressions by 2

• Subtract 7 from all three expressions

• Add 7 to all three expressions

What is the result after dividing all parts of the inequality 6 < 2x < 10 by 2?

• 3 <= x <= 5

• 3 <= x < 5

• 3 < x <= 5

• 3 < x < 5

How is the boundary point for 'less than' represented on a number line?

• Arrow to the left

• Arrow to the right

• Open circle

• Solid circle

What does the 'and' compound inequality graph look like on a number line?

• A single line with filled space between boundary points

• Two separate lines

• A dashed line

• A single line with arrows in opposite directions

In the 'or' type compound inequality, what is the result of solving y > -1?

• y <= -1

• y < -1

• y > -1

• y >= -1

How is the boundary point for 'greater than' represented on a number line?

• Arrow to the right

• Open circle

• Arrow to the left

• Solid circle

What is the key characteristic of the 'or' compound inequality graph?

• Arrows going in opposite directions

• A single line with filled space between boundary points

• Arrows going in the same direction

• A dashed line

How is the boundary line for y > -1 represented on a coordinate plane?

• Arrow to the left

• Arrow to the right

• Dashed line

• Solid line

Where do we shade for the inequality y < -7 on a coordinate plane?

• To the left of the line

• Above the line

• Below the line

• To the right of the line