Solving Inequalities and Their Properties

The video tutorial explains how to solve inequalities involving negative numbers. It begins by demonstrating a common mistake where the inequality sign is not flipped when dividing by a negative number. The correct approach is then shown, emphasizing the importance of flipping the inequality sign when multiplying or dividing by a negative number. An additional example is provided to reinforce the concept.

What is the first step in solving the inequality -3x < 27?

• Add 3 to both sides

• Multiply both sides by 3

• Subtract 3 from both sides

• Divide both sides by -3

Why is it incorrect to conclude that x < -9 when solving -3x < 27?

• Because x should be positive

• Because 27 is not divisible by -3

• Because dividing by a negative number requires flipping the inequality sign

• Because -3x is not a valid expression

What should you remember when dividing both sides of an inequality by a negative number?

• Keep the inequality sign the same

• Flip the inequality sign

• Subtract the same number from both sides

• Add the same number to both sides

If x > -9, which of the following values satisfies this inequality?

• -9

• -10

• -8

• -11

What is the first algebraic move to solve -3x + 6 <= 27?

• Add 6 to both sides

• Divide both sides by -3

• Subtract 6 from both sides

• Multiply both sides by 3

Why don't we flip the inequality sign when subtracting 6 from both sides in -3x + 6 <= 27?

• Because the inequality sign only flips when multiplying

• Because the inequality sign only flips when adding

• Because we are not dividing by a negative number

• Because subtraction does not affect the inequality sign

What is the final step to isolate x in the inequality -3x <= 21?

• Add 3 to both sides

• Multiply both sides by 3

• Subtract 3 from both sides

• Divide both sides by -3 and flip the inequality sign

What is the correct solution to the inequality -3x <= 21 after solving it?

• x >= 7

• x <= -7

• x >= -7

• x <= 7