Understanding Linear Inequalities

The video tutorial introduces linear inequalities, explaining how they differ from linear equations. It demonstrates how to check if a point is a solution to a linear inequality by substituting values and evaluating the resulting statement. Several examples are provided, including points (1, 2), (-3, -7), and (2, 2), to illustrate the process. Students are also given an exercise to determine if point (3, 6) is a solution, reinforcing the learning objectives.

What is the main difference between a linear inequality and a linear equation?

• A linear inequality has no variables.

• A linear inequality uses an equal sign.

• A linear inequality is always true.

• A linear inequality uses a greater than or less than symbol.

How do you check if a point is a solution to a linear inequality?

• By substituting the point into the inequality and checking if the statement is true.

• By graphing the inequality.

• By solving the inequality for x.

• By checking if the point lies on the x-axis.

What is the first step in checking if a point is a solution to a linear inequality?

• Check if the point is on the line.

• Solve the inequality for y.

• Graph the inequality.

• Substitute the point into the inequality.

For the inequality y > x - 3, is the point (1, 2) a solution?

• Yes, because 2 equals -2.

• Yes, because 2 is greater than -2.

• No, because 2 is less than -2.

• No, because 2 is not equal to -2.

What operation should be avoided when checking a point in a linear inequality?

• Dividing both sides by a positive number.

• Subtracting or adding from both sides.

• Multiplying both sides by a negative number.

• Adding the same number to both sides.

What is the result of the arithmetic operation in the example with point (1, 2)?

• 2 equals -2.

• 2 is not equal to -2.

• 2 is less than -2.

• 2 is greater than -2.

Why is the point (-3, -7) not a solution to the inequality y > x - 3?

• Because -7 equals -6.

• Because -7 is less than -6.

• Because -7 is not greater than -6.

• Because -7 is greater than -6.

What should you do after substituting a point into a linear inequality?

• Solve for y.

• Graph the inequality.

• Check if the resulting statement is true.

• Check if the point is on the line.

What is the arithmetic result when checking point (-3, -7)?

• -7 is not greater than -6.

• -7 equals -6.

• -7 is greater than -6.

• -7 is less than -6.

In the exercise, what values are substituted for x and y to check the point (3, 6)?

• x = 0, y = 0

• x = 1, y = 2

• x = 6, y = 3

• x = 3, y = 6