Solving and Analyzing Inequalities

This video tutorial covers solving multi-step inequalities, comparing them with one-step inequalities, and graphing solutions on a number line. It includes examples involving fractions and the use of distribution property. The lesson concludes with final examples to reinforce the concepts.

What is the main difference between one-step and multi-step inequalities?

• Multi-step inequalities involve only one operation.

• One-step inequalities require more steps to solve.

• One-step inequalities involve fractions.

• Multi-step inequalities require multiple operations to solve.

In the inequality x - 1 > 5, what is the solution for x?

• x > 5

• x > 7

• x > 6

• x > 4

What is the first step in solving the inequality 2x - 1 > 5?

• Add 1 to both sides

• Divide both sides by 2

• Subtract 1 from both sides

• Multiply both sides by 2

After solving 2x - 1 > 5, what is the value of x?

• x > 4

• x > 5

• x > 2

• x > 3

How is the solution set for x > 3 represented on a number line?

• An open circle at 3 and shading to the left

• A filled circle at 3 and shading to the left

• An open circle at 3 and shading to the right

• A filled circle at 3 and shading to the right

In the inequality 2m > 12, what is the solution for m?

• m > 6

• m > 8

• m > 7

• m > 5

What is the solution for d in the inequality d ≤ 5?

• d ≥ 5

• d > 5

• d < 5

• d ≤ 5

What is the first step in solving the inequality with fractions: 1/4x + 2/3 < 3/4?

• Divide both sides by 4

• Add 2/3 to both sides

• Subtract 2/3 from both sides

• Multiply both sides by 4

What is the result of 3/4 - 2/3?

• 1/3

• 1/6

• 1/4

• 1/12

In the inequality 0.2(x - 10) > -1.8, what is the first step?

• Add 10 to both sides

• Divide both sides by 0.2

• Subtract 10 from both sides

• Distribute 0.2 to the terms inside the parenthesis