Q: Given the inequality $$x \u003c 9$$, which of the following is the correct interval notation and graph representation?

$$(-\\infty, 9)$$ \\text{ with an open circle at 9}$

Q: Which interval notation represents all real numbers except $$5$$?

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

Q: If $$x$$ must satisfy $$x \\leq 0 or$$ $$x \u003e 5$$, which interval notation expresses the solution set?

$$(-\\infty, 0] \\cup (5, \\infty)$$

Q: Which interval notation represents the set of all $$x$$ such that $$x is $$less than $$-2 or $$greater than $$7$$?

$$(-\\infty, -2) \\cup (7, \\infty)$$

Question 1

Which of the following represents the interval notation for the solution set of $$-13 \leq x \leq 6$$?

Accepted Answer

$$[-13, 6]$$

Question 2

Given the inequality $$x \u003c 9$$, which of the following is the correct interval notation and graph representation?

Accepted Answer

$$(-\infty, 9)$$ \text{ with an open circle at 9}$

Question 3

Which interval notation correctly expresses the solution set for $$x \leq 7$$?

Accepted Answer

$$(-\infty, 7]$$

Question 4

If the solution to an inequality is $$x \u003e -8$$, how is this represented in interval notation?

Accepted Answer

$$(-8, \infty)$$

Question 5

Which of the following is a half-closed (half-open) interval?

Accepted Answer

$$[1, 5)$$

Question 6

Solve the inequality $$2x + 13 \u003e 19$$ and express the solution in interval notation.

Accepted Answer

$$(3, \infty)$$

Question 7

What is the solution set in interval notation for $$\frac{1}{2}(x + 1) \geq \frac{1}{2}(4 + 2x)$$?

Accepted Answer

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

Question 8

When solving $$-2x \u003c 6$$, what must you do to the inequality sign when dividing both sides by $$-2$$?

Accepted Answer

Reverse the inequality sign

Question 9

Which interval notation represents all real numbers except $$5$$?

Accepted Answer

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

Question 10

A chemical process requires the temperature $$T to be $$between $$20^\circC $$and $$80^\circC$$, inclusive. Which interval notation correctly expresses the acceptable temperature range?

Accepted Answer

$$[20, 80]$$

Question 11

Which of the following inequalities is equivalent to the interval $$[0, 5)$$?

Accepted Answer

$$0 \leq x \u003c 5$$

Question 12

A medication is effective for patients with blood pressure $$P$$ such that $$P \geq 120$$ and $$P \u003c 140. $$What is the interval notation for the effective range?

Accepted Answer

$$[120, 140)$$

Question 13

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

Accepted Answer

$$(-\infty, 12]$$

Question 14

Which interval notation represents all $$x$$ such that $$x is $$greater than or equal to $$-4$$?

Accepted Answer

$$[-4, \infty)$$

Question 15

If $$x$$ must satisfy $$x \leq 0 or$$ $$x \u003e 5$$, which interval notation expresses the solution set?

Accepted Answer

$$(-\infty, 0] \cup (5, \infty)$$

Question 16

A factory can operate safely if the pressure $$p is $$strictly between $$100$$ and $$250$$ psi. Which interval notation represents this?

Accepted Answer

$$(100, 250)$$

Question 17

Solve the inequality $$-4x + 8 \u003e 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 2)$$

Question 18

Which of the following is the correct interval notation for the solution set of $$x \geq -1$$ and $$x \leq 5$$?

Accepted Answer

$$[-1, 5]$$

Question 19

If a solution set is $$x \in [a, b)$$, which of the following statements is true?

Accepted Answer

$$x$$ can equal $$a$$ but not $$b$$

Question 20

Which interval notation represents the set of all $$x$$ such that $$x is $$less than $$-2 or $$greater than $$7$$?

Accepted Answer

$$(-\infty, -2) \cup (7, \infty)$$

Linear Inequalities and Interval Notation: Precalculus Study Notes

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