Graphing Compound Inequalities

The video tutorial explains how to solve and graph compound inequalities, focusing on 'and' and 'or' types. It provides step-by-step instructions for isolating variables and using interval notation. The 'and' inequalities are solved by finding a range between two values, while 'or' inequalities result in a split graph with solutions extending in opposite directions. The tutorial also covers graphing solutions on a number line and using interval notation to express solutions.

What are the two types of compound inequalities?

• Positive and Negative

• Greater and Less

• And and Or

• Equal and Not Equal

How is an 'and' compound inequality typically represented on a number line?

• With a split graph

• With a single boundary

• With boundaries on either end of a shaded area

• With no boundaries

In the example '21 < 6X + 3 < 27', what is the first step to isolate X?

• Divide by 6

• Multiply by 6

• Subtract 3 from each side

• Add 3 to each side

After isolating X in the inequality '21 < 6X + 3 < 27', what is the next step?

• Add 3 to each side

• Multiply by 6

• Subtract 3 from each side

• Divide by 6

What does interval notation '[3, 4]' indicate?

• X is between 3 and 4, including 3 and 4

• X is between 3 and 4, excluding 3 and 4

• X is greater than 3 and less than 4

• X is less than 3 and greater than 4

What type of graph is typically associated with an 'or' compound inequality?

• A single boundary graph

• A no boundary graph

• A split graph

• A shaded area graph

In the inequality '4n - 5 > 27', what is the first step to solve for n?

• Subtract 5 from each side

• Add 5 to each side

• Multiply by 4

• Divide by 4

What is the solution for n in the inequality '7n - 6 ≤ -41'?

• n ≤ -5

• n > -5

• n ≥ -5

• n < -5

How is the interval notation for 'n > 8' represented?

• (8, ∞)

• (8, ∞]

• [8, ∞)

• [8, ∞]

What does the interval notation '(-∞, -5]' indicate?

• n is less than or equal to -5

• n is less than -5

• n is greater than or equal to -5

• n is greater than -5