Q: Which of the following is the correct interval notation for all real numbers except $3$?

$(-\infty, 3) \cup (3, \infty)$

Question 1

Which of the following represents the solution set to the inequality $2x - 3 \leq 5$ in interval notation?

Accepted Answer

$(-\infty, 4]$

Question 2

Given the inequality $-4x > 12$, what is the correct solution set in set-builder notation?

Accepted Answer

$\{x \mid x > -3\}$

Question 3

Which of the following is the correct interval notation for the set $\{x \mid 2 < x \leq 7\}$?

Accepted Answer

$(2, 7]$

Question 4

A chemical process is safe if the temperature $T$ satisfies $-10 \leq T < 80$. Which interval notation correctly describes the set of safe temperatures?

Accepted Answer

$[-10, 80)$

Question 5

Which of the following is a linear inequality in one variable?

Accepted Answer

$5x - 4 \geq 2$

Question 6

When solving the inequality $-2x + 5 > 11$, what must you do when dividing both sides by $-2$?

Accepted Answer

Reverse the direction of the inequality symbol

Question 7

A university requires students to have a GPA $g$ such that $2.5 \leq g < 4.0$ to remain in good standing. Which set-builder notation describes this requirement?

Accepted Answer

$\{g \mid 2.5 \leq g < 4.0\}$

Question 8

Which of the following is the correct interval notation for all real numbers except $3$?

Accepted Answer

$(-\infty, 3) \cup (3, \infty)$

Question 9

Solve the compound inequality $1 < 2x + 3 \leq 7$ and express the solution in interval notation.

Accepted Answer

$(-1, 2]$

Question 10

Which of the following is the correct set-builder notation for the interval $(-\infty, 5]$?

Accepted Answer

$\{x \mid x \leq 5\}$

Question 11

A medication is effective for blood pressure $p$ in the range $120 < p \leq 140$. Which of the following correctly expresses this in interval notation?

Accepted Answer

$(120, 140]$

Question 12

Which of the following is NOT a correct way to represent the solution to $x > 2$?

Accepted Answer

$(-\infty, 2]$

Question 13

If $x$ is a solution to the inequality $3x - 7 < 2$, which of the following must be true?

Accepted Answer

$x < 3$

Question 14

Which of the following intervals represents all real numbers greater than or equal to $-2$?

Accepted Answer

$[-2, \infty)$

Question 15

A factory must keep the humidity $h$ between $30\%$ and $60\%$, inclusive. Which interval notation correctly describes the acceptable humidity levels?

Accepted Answer

$[30, 60]$

Question 16

Which of the following is the correct set-builder notation for the interval $[a, b)$?

Accepted Answer

$\{x \mid a \leq x < b\}$

Question 17

Which of the following is the correct solution to the inequality $5 - 2x \geq 1$?

Accepted Answer

$x \leq 2$

Question 18

A student must score at least $70$ but less than $90$ to pass a test. Which interval notation represents the passing scores?

Accepted Answer

$[70, 90)$

Question 19

Which of the following is the correct interval notation for all real numbers?

Accepted Answer

$(-\infty, \infty)$

Question 20

If $x$ satisfies $|x - 3| < 5$, what is the solution set in interval notation?

Accepted Answer

$(-2, 8)$

Polynomial and Rational Inequalities: Interval Notation, Set-Builder Notation, and Solution Methods

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