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 $$-4x \u003e 12$$, what is the correct solution set in set-builder notation?

Accepted Answer

$$\{x \mid x \u003e -3\}$$

Question 3

Which of the following is the correct interval notation for the set $$\{x \mid 2 \u003c x \leq 7\}$$?

Accepted Answer

$$(2, 7]$$

Question 4

A chemical process is safe if the temperature $$T$$ satisfies $$-10 \leq T \u003c 80. $$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 $$-2x + 5 \u003e 11$$, 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 $$2.5 \leq g \u003c 4.0 to $$remain in good standing. Which set-builder notation describes this requirement?

Accepted Answer

$$\{g \mid 2.5 \leq g \u003c 4.0\}$$

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 $$1 \u003c 2x + 3 \leq 7$$ 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 $$120 \u003c p \leq 140. $$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 $$x \u003e 2$$?

Accepted Answer

$$(-\infty, 2]$$

Question 13

If $$x is a $$solution to the inequality $$3x - 7 \u003c 2$$, which of the following must be true?

Accepted Answer

$$x \u003c 3$$

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

$$\{x \mid a \leq x \u003c b\}$$

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 $$|x - 3| \u003c 5$$, 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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