Question

Write the interval \((- \infty, 17]\) using an inequality and in set notation.

a. \(x \leq 17, \{x \mid x \leq 17\}\)

b. \(x < 17, \{x \mid x < 17\}\)

c. \(x \geq 17, \{x \mid x \geq 17\}\)

d. \(x > 17, \{x \mid x > 17\}\)

Answer 1

The interval (- ∞, 17] means x can be any number up to and including 17. The correct representations in inequality and set notation are x ≤ 17 and x ≤ 17, respectively.

Step-by-step explanation:

The question asks to write the interval (- ∞, 17] using an inequality and in set notation. The correct option that represents this interval in both an inequality and set notation is:

a. x ≤ 17, x ≤ 17

The interval notation (- ∞, 17] indicates that x can be any real number up to and including 17 but not less than negative infinity. In inequality form, this is written as x ≤ 17, which reads as 'x is less than or equal to 17.' In set notation, this interval is represented as x , meaning 'the set of all x such that x is less than or equal to 17.'