Solving and Verifying Inequalities

The video tutorial explains how to solve the linear inequality 3x + 6 ≥ 15. It begins by introducing the concept of solving inequalities similarly to equations, with a special rule for when multiplying or dividing by negative numbers, which requires flipping the inequality sign. The tutorial then provides a step-by-step solution, starting with subtracting 6 from both sides and then dividing by 3, resulting in x ≥ 3. The solution is matched to the correct answer choice.

What is the special rule to remember when solving inequalities involving multiplication or division?

• Always add a constant to both sides.

• Multiply both sides by zero.

• Flip the inequality sign when multiplying or dividing by a negative number.

• Subtract a constant from both sides.

What is the first step in isolating the variable in the inequality 3x + 6 ≥ 15?

• Subtract 6 from both sides.

• Multiply both sides by 3.

• Divide both sides by 3.

• Add 6 to both sides.

After subtracting 6 from both sides of the inequality 3x + 6 ≥ 15, what is the resulting inequality?

• 3x ≥ 21

• 3x ≥ 9

• 3x ≤ 21

• 3x ≤ 9

What operation is performed to both sides of the inequality 3x ≥ 9 to solve for x?

• Subtract 3 from both sides.

• Add 3 to both sides.

• Multiply both sides by 3.

• Divide both sides by 3.

What is the solution to the inequality 3x ≥ 9?

• x ≤ 9

• x ≥ 3

• x ≤ 3

• x ≥ 9

How do you verify the solution to an inequality?

• By using a calculator.

• By checking if the solution satisfies the original inequality.

• By solving a different inequality.

• By graphing the solution.

Which answer choice matches the solution x ≥ 3?

• Choice B

• Choice C

• Choice A

• Choice D