Exploring Compound Inequalities and Their Graphs

The video tutorial explains how to solve and graph compound inequalities. It covers solving two inequalities separately and then combining their solution sets based on 'or' and 'and' conditions. The tutorial includes examples and demonstrates graphing solutions on a number line, highlighting the importance of open and closed circles. It emphasizes understanding the difference between 'or' and 'and' in compound inequalities and how to find the solution set accordingly.

What is a compound inequality?

• Two or more inequalities combined

• An equation with two variables

• An inequality with only one variable

• A single inequality with a constant

What is the first step in solving the inequality 2x - 6 < -14?

• Multiply both sides by 2

• Add 6 to both sides

• Subtract 6 from both sides

• Divide both sides by 2

After solving 2x - 6 < -14, what is the value of x?

• x > -4

• x > -8

• x < -4

• x < -8

How is the solution x < -4 represented on a number line?

• Open circle on -4, shading to the left

• Closed circle on -4, shading to the right

• Open circle on -4, shading to the right

• Closed circle on -4, shading to the left

What is the first step in solving the inequality 2x + 3 ≤ 1?

• Subtract 3 from both sides

• Add 3 to both sides

• Multiply both sides by 2

• Divide both sides by 2

After solving 2x + 3 ≤ 1, what is the value of x?

• x ≤ -2

• x ≥ -2

• x ≤ -1

• x ≥ -1

How is the solution x ≤ -1 represented on a number line?

• Closed circle on -1, shading to the left

• Open circle on -1, shading to the left

• Open circle on -1, shading to the right

• Closed circle on -1, shading to the right

What happens when combining graphs for 'or' conditions?

• Only the overlap is shaded

• Both graphs are shaded completely

• Neither graph is shaded

• Only one graph is shaded

What happens when combining graphs for 'and' conditions?

• Neither graph is shaded

• Only one graph is shaded

• Both graphs are shaded completely

• Only the overlap is shaded

When solving 9 ≥ -5x + 3, what must you remember when dividing by a negative number?

• Subtract the negative number from both sides

• Keep the inequality sign the same

• Flip the inequality sign

• Add the negative number to both sides