Understanding Interval Notation and Inequalities

Which of the following represents the interval notation for all numbers greater than 3 and less than or equal to 7?

Answer explanation

The interval notation (3, 7] indicates that numbers greater than 3 are included (3 is not included) and numbers up to and including 7 are included. Thus, (3, 7] correctly represents all numbers greater than 3 and less than or equal to 7.

Answer explanation

The inequality -2 ≤ x < 5 indicates that -2 is included (hence the bracket [) and 5 is not included (hence the parenthesis ). Therefore, the correct interval notation is [-2, 5).

• A line extending to the left from 4 with an open circle at 4

• A line extending to the left from 4 with a closed circle at 4

• A line extending to the right from 4 with an open circle at 4

• A line extending to the right from 4 with a closed circle at 4

Answer explanation

The interval (-∞, 4] includes all numbers less than or equal to 4. This is represented by a line extending to the left from 4 with a closed circle at 4, indicating that 4 is included in the interval.

Answer explanation

The union of the intervals (-∞, 2) and (1, 5] includes all numbers less than 2 and all numbers greater than 1 up to 5. Thus, it covers all numbers up to 5, leading to the correct answer: (-∞, 5].

Answer explanation

To solve the inequality 3x - 1 ≤ 8, add 1 to both sides to get 3x ≤ 9. Then, divide by 3 to find x ≤ 3. In interval notation, this is expressed as (-∞, 3]. Thus, the correct answer is (-∞, 3].

Look at the graph. Write the inequality in interval notation.

• (-2,5)

• (-∞,-2)⋃(5,∞)

• [-2,5]

• (-∞,-2]∪[5,∞)

What is the interval notation for this graph?

Write in interval notation: 3 < x ≤ 5

• [3, 5]

• [3, 5)

• (3, 5]

• (-∞, 8]

• (3, 5)

Write the following solution in interval notation:

z < 20

• ( -∞ , 20 )

• ( 20,∞)

• ( -∞ , 20)

• ( -∞ , 20]

Convert the inequality -2 ≤ y < 7 to interval notation.

• (-2, 7)

• [-2, 7)

• (-2, 7]

• [-2, 7]