Understanding Compound Inequalities

The video tutorial explains how to solve a compound inequality involving the expression -16 ≤ 3x + 5 ≤ 20. It demonstrates rewriting the inequality as two separate inequalities, solving them, and graphing the solution on a number line. The tutorial also verifies the solution by testing sample points to ensure they satisfy the original inequality.

What is the initial compound inequality given in the problem?

• -16 ≤ 3x + 5 ≤ 20

• -16 < 3x + 5 < 20

• -16 > 3x + 5 > 20

• -16 ≥ 3x + 5 ≥ 20

How can the compound inequality be split into two separate inequalities?

• -16 < 3x + 5 and 3x + 5 < 20

• -16 ≥ 3x + 5 and 3x + 5 ≥ 20

• -16 ≤ 3x + 5 and 3x + 5 ≤ 20

• -16 > 3x + 5 and 3x + 5 > 20

What operation is performed on all parts of the inequality to isolate x?

• Subtract 5

• Add 5

• Multiply by 3

• Divide by 3

After subtracting 5 from all parts, what is the new inequality?

• -21 ≤ 3x ≤ 15

• -21 < 3x < 15

• -21 ≥ 3x ≥ 15

• -21 > 3x > 15

What is the final solution for x after dividing by 3?

• -7 ≥ x ≥ 5

• -7 > x > 5

• -7 < x < 5

• -7 ≤ x ≤ 5

How is the solution set represented on a number line?

• A line segment from -7 to 5, excluding both endpoints

• A line segment from -7 to 5, including both endpoints

• A line segment from -7 to 5, including only -7

• A line segment from -7 to 5, including only 5

Which of the following values is part of the solution set?

• 6

• 0

• 10

• 8

Why does the value 6 not satisfy the inequality?

• Because 23 is not ≥ 20

• Because 23 is not ≤ 20

• Because 23 is not < 20

• Because 23 is not > 20

What happens when you test the value 8 in the inequality?

• It satisfies the inequality because -19 is ≤ 20

• It does not satisfy the inequality because -19 is not ≥ -16

• It satisfies the inequality

• It does not satisfy the inequality because -19 is not ≤ -16

What is the purpose of testing values like 0, 6, and 8 in the inequality?

• To change the inequality

• To simplify the inequality

• To find new solutions

• To verify the accuracy of the solution set