Question 1

Which of the following represents the interval notation for the solution set $\{ x \mid -3 < x \leq 5 \}$?

Accepted Answer

$(-3, 5]$

Question 2

Given the inequality $2x - 6 < 0$, what is the solution in interval notation?

Accepted Answer

$(-\infty, 3)$

Question 3

Which of the following correctly expresses the set $\{ x \mid x \geq 0 \}$ in interval notation?

Accepted Answer

$[0, \infty)$

Question 4

Solve the inequality $2x + 4 \geq 10$ and express the solution in interval notation.

Accepted Answer

$[3, \infty)$

Question 5

Which of the following is the correct interval notation for all real numbers less than or equal to $7$?

Accepted Answer

$(-\infty, 7]$

Question 6

If $x$ satisfies $0 < x < 5$, which of the following is the correct interval notation?

Accepted Answer

$(0, 5)$

Question 7

Solve the inequality $-2x \geq 8$ and express the solution in interval notation.

Accepted Answer

$(-\infty, -4]$

Question 8

Which of the following best describes the solution set for $x \leq 0$ in set-builder notation?

Accepted Answer

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

Question 9

A chemical process is safe only if the temperature $T$ is between $14$ and $26$ degrees Celsius, inclusive. Which interval notation represents the safe temperature range?

Accepted Answer

$[14, 26]$

Question 10

Solve the inequality $\frac{1}{4}(x + 2) \geq \frac{1}{12} - \frac{1}{3}x$ and express the solution in interval notation.

Accepted Answer

$[12, \infty)$

Question 11

Which of the following is the correct interval notation for the set $\{ x \mid x > 0 \}$?

Accepted Answer

$(0, \infty)$

Question 12

A medication is effective for blood pressure values $x$ such that $114 \leq x < 126$. Which interval notation represents the effective range?

Accepted Answer

$[114, 126)$

Question 13

Solve the inequality $2x + 12 > 19$ and express the solution in interval notation.

Accepted Answer

$(3.5, \infty)$

Question 14

Which of the following is the correct interval notation for the set $\{ x \mid x \leq 7 \}$?

Accepted Answer

$(-\infty, 7]$

Question 15

Solve the inequality $\frac{5}{3}(x + 1) \geq \frac{5}{3}(3 + 2x)$ and express the solution in interval notation.

Accepted Answer

$(-\infty, 2]$

Question 16

A company only hires applicants aged between $18$ and $65$, inclusive. Which interval notation represents the eligible age range?

Accepted Answer

$[18, 65]$

Question 17

Which of the following is the correct interval notation for the set $\{ x \mid x < 0 \}$?

Accepted Answer

$(-\infty, 0)$

Question 18

Solve the inequality $3x - 7 \leq 2x + 5$ and express the solution in interval notation.

Accepted Answer

$(-\infty, 12]$

Question 19

Which of the following is the correct interval notation for the set $\{ x \mid x \geq -2 \}$?

Accepted Answer

$[-2, \infty)$

Question 20

A water filter is effective for pH values $x$ such that $6 < x \leq 8$. Which interval notation represents the effective pH range?

Accepted Answer

$(6, 8]$

Interval Notation and Solving Linear Inequalities

Study Guide - Practice Questions

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