Understanding Inequalities

The video tutorial explores two inequalities: x + 2 ≤ 2x and 3x + 4 > 5x. The instructor tests four numbers (0, 1, 2, and 5) to see if they satisfy either inequality. Zero and one satisfy the second inequality, while two and five satisfy the first. The video demonstrates that inequalities can have multiple solutions, no solutions, or infinite solutions.

What are the two inequalities discussed in the video?

• x + 2 > 2x and 3x + 4 ≤ 5x

• x + 2 ≤ 2x and 3x + 4 > 5x

• x + 2 ≥ 2x and 3x + 4 < 5x

• x + 2 < 2x and 3x + 4 ≥ 5x

Does the number zero satisfy the inequality x + 2 ≤ 2x?

• Yes, because 2 is less than or equal to 0

• No, because 2 is not less than or equal to 0

• Yes, because 0 is less than or equal to 2

• No, because 0 is not less than or equal to 2

Does the number zero satisfy the inequality 3x + 4 > 5x?

• Yes, because 4 is greater than 0

• No, because 4 is not greater than 0

• Yes, because 0 is greater than 4

• No, because 0 is not greater than 4

Does the number one satisfy the inequality x + 2 ≤ 2x?

• Yes, because 2 is less than or equal to 3

• No, because 3 is not less than or equal to 2

• No, because 2 is not less than or equal to 3

• Yes, because 3 is less than or equal to 2

Does the number one satisfy the inequality 3x + 4 > 5x?

• No, because 5 is not greater than 7

• Yes, because 5 is greater than 7

• No, because 7 is not greater than 5

• Yes, because 7 is greater than 5

Does the number two satisfy the inequality x + 2 ≤ 2x?

• Yes, because 4 is less than or equal to 4

• No, because 4 is not less than or equal to 4

• Yes, because 2 is less than or equal to 4

• No, because 2 is not less than or equal to 4

Does the number two satisfy the inequality 3x + 4 > 5x?

• Yes, because 6 is greater than 10

• No, because 6 is not greater than 10

• Yes, because 10 is greater than 10

• No, because 10 is not greater than 10

Does the number five satisfy the inequality x + 2 ≤ 2x?

• No, because 7 is not less than or equal to 10

• No, because 10 is not less than or equal to 7

• Yes, because 10 is less than or equal to 7

• Yes, because 7 is less than or equal to 10

Does the number five satisfy the inequality 3x + 4 > 5x?

• Yes, because 19 is greater than 25

• No, because 25 is not greater than 19

• Yes, because 25 is greater than 19

• No, because 19 is not greater than 25

Which numbers satisfy the inequality x + 2 ≤ 2x?

• One and two

• Zero and one

• Two and five

• Zero and five