Solving Compound Inequalities

The video tutorial explains how to solve a compound inequality, negative 16 ≤ 3x + 5 ≤ 20, using two approaches: solving it as a single compound inequality and breaking it into two separate inequalities. The tutorial demonstrates isolating the variable x by subtracting 5 and dividing by 3, resulting in the solution set -7 ≤ x ≤ 5. The solution is then graphed on a number line, and its validity is verified by testing values within and outside the solution set.

What is the compound inequality given in the problem?

• 3x + 5 < -16 < 20

• -16 >= 3x + 5 >= 20

• -16 <= 3x + 5 <= 20

• 3x + 5 > -16 > 20

How can the compound inequality be viewed alternatively?

• As two separate inequalities

• As a quadratic equation

• As a linear equation

• As a single inequality

What is the first step in isolating x in the compound inequality?

• Divide each part by 3

• Subtract 5 from each part

• Multiply each part by 3

• Add 5 to each part

After subtracting 5 from each part, what is the resulting inequality?

• -21 <= 3x <= 15

• -21 >= 3x >= 15

• -21 < 3x < 15

• -21 > 3x > 15

What operation is performed after subtracting 5 to further simplify the inequality?

• Divide by 3

• Add 3

• Multiply by 3

• Subtract 3

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

• -7 < x < 5

• -7 >= x >= 5

• -7 <= x <= 5

• -7 > x > 5

Which number is part of the solution set?

• 10

• 6

• 0

• 8

What happens when you test the number 10 in the inequality?

• It is equal to the boundary

• It is less than the boundary

• It does not satisfy the inequality

• It satisfies the inequality

Which of the following is NOT a correct step in solving the compound inequality?

• Subtract 5 from each part

• Divide each part by 3

• Isolate x

• Add 5 to each part

What is the purpose of verifying the solution set?

• To change the inequality

• To ensure the solution set is correct

• To find new solutions

• To solve a different problem