Solving One-Step Inequalities: Key Concepts and Examples

The video tutorial by Mr. J covers how to solve one-step inequalities, which are similar to one-step equations. The key difference is the number of solutions: inequalities can have infinite solutions, while equations have one. The tutorial includes four examples demonstrating how to isolate variables using inverse operations and emphasizes the importance of flipping the inequality sign when multiplying or dividing by a negative number. Each example is tested to confirm the solution, and the video concludes with a brief explanation of why flipping the sign is necessary.

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

• Inequalities can only be solved by adding or subtracting.

• Equations do not involve variables.

• Equations are harder to solve than inequalities.

• Inequalities have multiple solutions, while equations have a single solution.

What does isolating the variable in an inequality involve?

• Ignoring the inequality sign

• Only multiplying both sides by the same number

• Only adding numbers to both sides

• Performing the same operation on both sides

What operation is used to isolate the variable in the inequality 'y + 7 < 8'?

• Multiplication

• Division

• Subtraction

• Addition

What is the correct solution when testing 'y < 1' with y = 0?

• 0 + 7 ≠ 8 is true

• 0 + 7 = 8 is true

• 0 + 7 > 8 is true

• 0 + 7 < 8 is true

What is the solution to the inequality 'x/5 ≥ 3'?

• x ≤ 15

• x > 15

• x ≥ 15

• x < 15

Which of the following is a valid solution for 'x ≥ 15'?

• x = -15

• x = 10

• x = 20

• x = 14

In the inequality '14 ≥ n - 11', what operation is performed to both sides to isolate 'n'?

• Subtraction

• Multiplication

• Division

• Addition

For the inequality '25 ≥ n', which of the following is a correct solution?

• n = 26

• n = 25

• n = 24

• n = -25

Why do we flip the inequality sign when dividing both sides by a negative number?

• To make the inequality false

• Because it's a rule without a reason

• To get more solutions

• To maintain the balance of the inequality

What is the result of solving the inequality '-6r < 36'?

• r ≥ -6

• r ≤ -6

• r < -6

• r > -6