Solving Compound Inequalities Challenge

The video tutorial covers solving and graphing compound inequalities, focusing on 'and' and 'or' inequalities. It explains two methods for solving 'and' inequalities, including a preferred method and an alternative. The tutorial also addresses solving 'or' inequalities and highlights special cases where solutions may not be as expected. Throughout, the instructor emphasizes the importance of balancing equations and graphing solutions accurately.

What is a compound inequality?

• An equation with no inequalities

• A single inequality with multiple variables

• Two inequalities joined by 'and' or 'or'

• An equation with one inequality

In the three-section method, what must you do to keep the inequality balanced?

• Only change one section

• Change all three sections equally

• Change two sections equally

• Do nothing

When solving 'and' inequalities by splitting them, what must you remember to do when dividing by a negative number?

• Keep the inequality sign the same

• Flip the inequality sign

• Add the same number to both sides

• Subtract the same number from both sides

What is the first step in solving an 'or' compound inequality?

• Graph the inequalities first

• Solve each inequality separately

• Combine the inequalities

• Ignore one of the inequalities

When graphing 'or' compound inequalities, where do you place the solutions?

• On a bar chart

• On the same number line

• On separate number lines

• On a graph with two axes

What happens when the solutions of an 'and' inequality do not overlap?

• There is no solution

• There is one solution

• There are infinite solutions

• The solution is the entire number line

In special cases of 'or' inequalities, what can happen to the solution?

• It can be a fraction

• It can be a complex number

• It can have no solution

• It can be simplified to a single inequality

What is the final step after solving a compound inequality?

• Checking the solution

• Graphing the solution

• Rewriting the inequality

• Ignoring the solution

When graphing an 'and' inequality, what do you graph?

• The sum of the solutions

• The difference of the solutions

• The intersection of the solutions

• The union of the solutions

What should you do if you encounter a negative variable in an inequality?

• Leave it as is

• Divide by a negative number and flip the sign

• Add a positive number

• Subtract a positive number