Question 1

Which of the following represents the interval notation for all real numbers $$x$$ such that $$x \u003c 5$$?

Accepted Answer

$$(-\infty, 5)$$

Question 2

A farmer wants to market her fruit as 'organic.' According to regulations, the soil must be pesticide-free for at least three years. Let $$t be $$the number of years the soil has been pesticide-free. Which inequality correctly represents this requirement?

Accepted Answer

$$t \geq 3$$

Question 3

Which set notation correctly represents the interval $$[2, 4)$$?

Accepted Answer

$$\{ x \mid 2 \leq x \u003c 4 \}$$

Question 4

Solve the inequality $$5x - 9 \u003c 1$$ and express your answer in interval notation.

Accepted Answer

$$(-\infty, 2)$$

Question 5

Which of the following intervals represents all real numbers $$x$$ such that $$x \geq 1$$?

Accepted Answer

$$[1, \infty)$$

Question 6

Shade the interval $$[−2, 1) \cup (2, \infty) on $$the number line. Which of the following best describes the union of these intervals?

Accepted Answer

$$[−2, 1) \cup (2, \infty)$$

Question 7

Solve the inequality $$-5x + 1 \leq 2$$ and express your answer in interval notation.

Accepted Answer

$$(-\infty, -\frac{1}{5}]$$

Question 8

Which inequality corresponds to the interval notation $$(−\infty, 0]$$?

Accepted Answer

$$x \leq 0$$

Question 9

Solve the inequality $$\frac{1}{3}(x - 9) \u003e 2$$ and express your answer in interval notation.

Accepted Answer

$$(15, \infty)$$

Question 10

Which of the following is the correct set notation for the interval $$[2, \infty)$$?

Accepted Answer

$$\{ x \mid x \geq 2 \}$$

Question 11

Which interval notation represents all real numbers $$x$$ such that $$1 \leq x \u003c 3$$?

Accepted Answer

$$[1, 3)$$

Question 12

A soil sample has been pesticide-free for $$t$$ years. If the requirement is $$t \u003e 3$$, which interval notation represents the eligible years?

Accepted Answer

$$(3, \infty)$$

Question 13

Which of the following is the correct interval notation for the solution to $$3 + 7x + 5 \geq 17$$?

Accepted Answer

$$[1, \infty)$$

Question 14

Which of the following intervals represents the union of $$(−\infty, 1) \cup (2, 3) \cup (6, \infty)$$?

Accepted Answer

$$(−\infty, 1) \cup (2, 3) \cup (6, \infty)$$

Question 15

Which inequality corresponds to the interval notation $$(−\infty, 0)$$?

Accepted Answer

$$x \u003c 0$$

Question 16

A company requires that employees have worked for at least 2 years to qualify for a bonus. Which interval notation represents the eligible years?

Accepted Answer

$$[2, \infty)$$

Question 17

Which set notation represents the interval $$(−\infty, 0]$$?

Accepted Answer

$$\{ x \mid x \leq 0 \}$$

Question 18

Which interval notation represents all real numbers $$x$$ such that $$x \u003c 1$$?

Accepted Answer

$$(-\infty, 1)$$

Question 19

If a medical study requires participants to be at least 18 years old, which inequality and interval notation represent this requirement?

Accepted Answer

$$x \geq 18$$; $$[18, \infty)$$

Question 20

Which interval notation represents all real numbers $$x$$ such that $$x \u003e 2$$?

Accepted Answer

$$(2, \infty)$$

Precalculus Study Guide: Interval Notation & Solving Inequalities

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