Solving Inequalities and Their Properties

The video tutorial covers solving inequalities, focusing on the impact of negative numbers. It begins with a review of basic inequalities and transitions to solving them when negatives are involved. The tutorial emphasizes the importance of reversing the inequality sign when multiplying or dividing by a negative number. Several examples are provided to illustrate these concepts, ensuring a clear understanding of how to handle inequalities with negative coefficients.

What is the main focus of the lesson on inequalities?

• Graphing linear equations

• Understanding inequalities with negative numbers

• Solving quadratic equations

• Solving equations with fractions

When solving the inequality 6x < 12, what is the first step?

• Divide both sides by 6

• Subtract 6 from both sides

• Multiply both sides by 6

• Add 6 to both sides

How is the solution x < 2 represented on a number line?

• An open circle at 2 with a line extending to the right

• A filled circle at 2 with a line extending to the left

• An open circle at 2 with a line extending to the left

• A filled circle at 2 with a line extending to the right

If x = 1 is substituted back into the inequality 6x < 12, what is the result?

• 6 is not comparable to 12

• 6 is less than 12

• 6 is equal to 12

• 6 is greater than 12

What happens to the inequality sign when you multiply or divide by a negative number?

• It becomes a greater than sign

• It flips direction

• It becomes an equal sign

• It stays the same

When solving -6x < 12, what is the correct solution for x?

• x = -2

• x > 2

• x < -2

• x > -2

In the inequality -7W ≤ 21, what must be done to solve for W?

• Subtract 7 from both sides

• Add 7 to both sides

• Divide both sides by -7 and flip the inequality sign

• Multiply both sides by 7

What is the solution to the inequality -3H > -12 after dividing by -3?

• H ≥ 4

• H ≤ 4

• H > 4

• H < 4

What is the first step in solving the inequality with a denominator?

• Subtract the denominator from both sides

• Multiply both sides by the denominator

• Add the denominator to both sides

• Divide both sides by the denominator