Understanding Compound Inequalities

The video tutorial explains how to solve a compound inequality involving two conditions: 5z + 7 < 27 and -3z <= 18. It demonstrates solving each inequality separately, combining the solutions, and visualizing them on a number line. The tutorial emphasizes that z can satisfy either condition, resulting in a solution set that covers the entire number line. Examples are provided to test the constraints and illustrate the solution set.

What type of inequality is being solved in the video?

• Quadratic inequality

• Simple inequality

• Absolute value inequality

• Compound inequality

What is the first step in solving the inequality 5z + 7 < 27?

• Add 7 to both sides

• Multiply both sides by 5

• Divide both sides by 5

• Subtract 7 from both sides

After isolating 5z, what is the next step to solve 5z < 20?

• Add 5 to both sides

• Divide both sides by 5

• Multiply both sides by 5

• Subtract 5 from both sides

When solving -3z ≤ 18, why must the inequality sign be swapped?

• Because we are multiplying by a positive number

• Because we are dividing by a negative number

• Because we are adding a negative number

• Because we are subtracting a positive number

What is the solution to the inequality -3z ≤ 18?

• z < -6

• z > -6

• z ≤ -6

• z ≥ -6

What does the solution set z < 4 or z ≥ -6 represent?

• z must satisfy both conditions

• z must satisfy neither condition

• z must satisfy at least one condition

• z must satisfy exactly one condition

How is the solution set represented on a number line?

• As a single point

• As a single interval

• As two separate intervals

• As the entire number line

Which number satisfies both inequalities?

• -7

• 0

• 5

• 4

Why does the number 4 only satisfy one of the inequalities?

• Because 4 is greater than 27

• Because -3 times 4 is greater than 18

• Because 4 is less than -6

• Because 5 times 4 plus 7 equals 27

What is the significance of the 'or' condition in the solution set?

• It means z must satisfy both conditions

• It means z must satisfy exactly one condition

• It means z must satisfy neither condition

• It means z must satisfy at least one condition