Question 1

Which of the following represents the solution set for the inequality $$3x - 7 \u003c 5 in $$interval notation?

Accepted Answer

$$(-\infty, 4)$$

Question 2

If $$x is in $$the interval $$[2, 5)$$, which of the following is the correct set-builder notation for this interval?

Accepted Answer

$$\{x\mid 2 \leq x \u003c 5\}$$

Question 3

Which of the following intervals includes all real numbers less than or equal to $$-3$$?

Accepted Answer

$$(-\infty, -3]$$

Question 4

Given the intervals $$[1, 4]$$ and $$(3, 6)$$, what is their intersection?

Accepted Answer

$$(3, 4]$$

Question 5

Solve the compound inequality $$-2 \u003c 2x + 4 \u003c 8$$ and express the solution in interval notation.

Accepted Answer

$$(-3, 2)$$

Question 6

Which of the following is true about the interval $$(-\infty, 7)$$?

Accepted Answer

It contains all real numbers less than $$7$$ but not $$7$$ itself.

Question 7

Solve the absolute value inequality $$|2x - 5| \u003c 9$$ and write the solution in interval notation.

Accepted Answer

$$(-2, 7)$$

Question 8

Which of the following statements is correct when multiplying both sides of an inequality by a negative number?

Accepted Answer

The direction of the inequality symbol must be reversed.

Question 9

A toll bridge charges $$5 per crossing, or you can buy a 25 $$decal for a 25% discount per crossing. For which number of crossings is the decal the better deal?

Accepted Answer

$$x \u003e 20$$

Question 10

Solve the absolute value inequality $$|x + 3| \u003e 7$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -10) \cup (4, \infty)$$

Question 11

Which interval notation correctly represents all real numbers except $$2$$ and $$5$$?

Accepted Answer

$$(-\infty, 2) \cup (2, 5) \cup (5, \infty)$$

Question 12

If $$x$$ satisfies $$|4x - 8| \leq 12$$, what is the solution set in interval notation?

Accepted Answer

$$[-1, 5]$$

Question 13

Which of the following is the union of the intervals $$(-\infty, 2]$$ and $$[5, \infty)$$?

Accepted Answer

$$(-\infty, 2] \cup [5, \infty)$$

Question 14

A chemical process is safe for temperatures in the interval $$[60, 120]$$ degrees Celsius. Which set-builder notation describes the safe temperature range?

Accepted Answer

$$\{x\mid 60 \leq x \leq 120\}$$

Question 15

Solve the inequality $$-4x + 8 \geq 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 16

Which of the following intervals represents all real numbers greater than $$-5$$ and less than or equal to $$3$$?

Accepted Answer

$$(-5, 3]$$

Question 17

If $$|x| \u003c 4$$, which of the following is the correct solution set?

Accepted Answer

$$(-4, 4)$$

Question 18

A medical test is valid for ages between $$18$$ and $$65$$, inclusive. Which interval notation represents the valid age range?

Accepted Answer

$$[18, 65]$$

Question 19

Solve the inequality $$5 - 2x \u003e 11$$ and express the solution in interval notation.

Accepted Answer

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

Question 20

Which of the following is the correct interval notation for all real numbers except those between $$-2$$ and $$5$$, not including $$-2$$ and $$5$$?

Accepted Answer

$$(-\infty, -2] \cup [5, \infty)$$

Linear and Absolute Value Inequalities: Interval Notation and Solution Methods

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