Question 1

Which of the following represents the interval of all real numbers greater than 2, using interval notation?

Accepted Answer

$$(2, \infty)$$

Question 2

What is the solution set in interval notation for the inequality $$3x - 5 \u003c 10$$?

Accepted Answer

Question 3

Solve the compound inequality $$-2 \u003c x + 1 \leq 4$$ and express the solution in interval notation.

Accepted Answer

$$(-3, 3]$$

Question 4

Which of the following is the correct set-builder notation for the interval $$[1, 3.5]$$?

Accepted Answer

$$\{ x \mid 1 \leq x \leq 3.5 \}$$

Question 5

If $$x$$ satisfies $$|x - 2| \u003c 5$$, what is the solution set in interval notation?

Accepted Answer

$$(-3, 7)$$

Question 6

Which of the following statements is true about the intersection of $$[1, 3]$$ and $$(2, 6)$$?

Accepted Answer

$$(2, 3]$$

Question 7

Solve the inequality $$-4x \u003e 12$$ and express the solution in interval notation.

Accepted Answer

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

Question 8

Which of the following intervals represents all real numbers less than or equal to $$b$$?

Accepted Answer

$$(-\infty, b]$$

Question 9

If $$|2x + 1| \geq 7$$, what is the solution set in interval notation?

Accepted Answer

$$(-\infty, -4] \cup [3, \infty)$$

Question 10

Which of the following is the union of the intervals $$[2, 5)$$ and $$(4, 7]$$?

Accepted Answer

$$[2, 5) \cup (4, 7]$$

Question 11

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

Accepted Answer

$$[2, \infty)$$

Question 12

Which of the following is true about the solution to $$2(x - 3) \u003e 2x - 6$$?

Accepted Answer

No solution (the inequality is never true)

Question 13

If $$|x + 4| \leq 3$$, what is the solution set in interval notation?

Accepted Answer

$$[-7, -1]$$

Question 14

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

Accepted Answer

$$(-\infty, \infty)$$

Question 15

Solve the compound inequality $$2 \u003c 3x + 1 \u003c 8$$ and express the solution in interval notation.

Accepted Answer

$$(\frac{1}{3}, \frac{7}{3})$$

Question 16

Which of the following is the correct way to write the interval of all real numbers greater than or equal to $$-2$$?

Accepted Answer

$$[-2, \infty)$$

Linear Inequalities and Absolute Value Inequalities: Study Notes

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