Question 1

Which of the following represents the interval notation for all real numbers $$x$$ such that $$-3 \u003c x \u003c 0$$?

Accepted Answer

$$( -3, 0 )$$

Question 2

Write the interval $$[0, 3) as an $$inequality involving $$x.$$

Accepted Answer

$$0 \leq x \u003c 3$$

Question 3

If $$x \u003e 4$$, what is the result of $$x + (-4)$$ compared to $$0$$?

Accepted Answer

$$x - 4 \u003e 0$$

Question 4

Which property of inequalities states that if $$a  0$$, then $$ac \u003c bc$$?

Accepted Answer

Multiplication Property of Inequalities

Question 5

Solve the inequality $$5 - 4x \u003c 9$$ and express the solution in interval notation.

Accepted Answer

$$( -1, \infty )$$

Question 6

Which of the following is the correct interval notation for $$x \leq 5$$?

Accepted Answer

$$( -\infty, 5 ]$$

Question 7

If $$8 \u003e 3$$, what is the result of multiplying both sides by $$-2$$?

Accepted Answer

$$-16 \u003c -6$$

Question 8

Solve the combined inequality $$4 \u003c 2x + 2 \u003c 10$$ and express the solution in interval notation.

Accepted Answer

$$( 1, 4 )$$

Question 9

Which of the following procedures will reverse the direction of an inequality symbol?

Accepted Answer

Multiplying both sides by a negative number

Question 10

An air-conditioning unit has a resistance of $$10$$ ohms. If the voltage varies from $$90 to$$ $$110$$ volts, inclusive, what is the range of current (in amperes) the unit will draw? (Use Ohm’s Law: $$E = IR)$$

Accepted Answer

$$[9, 11]$$

Question 11

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

Accepted Answer

$$[5, \infty)$$

Question 12

Which of the following is the correct inequality for the interval $$(3, \infty)$$?

Accepted Answer

$$x \u003e 3$$

Question 13

If $$-4 \u003c x \u003c 0$$, what is the equivalent inequality for $$\frac{x}{2}$$?

Accepted Answer

$$-2 \u003c \frac{x}{2} \u003c 0$$

Question 14

Solve the inequality $$(2x - 4$$)^{-1}$$ \u003e 0$$ and express the solution in interval notation.

Accepted Answer

$$(2, \infty)$$

Question 15

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

Accepted Answer

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

Question 16

If $$-5x \u003c -10$$, what is the solution for $$x$$?

Accepted Answer

$$x \u003e 2$$

Question 17

Which of the following is the correct inequality for the interval $$[3, 4]$$?

Accepted Answer

$$3 \leq x \leq 4$$

Question 18

Solve the combined inequality $$-3 \leq \frac{x + 2}{-2} \u003c 1$$ and express the solution in interval notation.

Accepted Answer

$$[ -6, 0 ]$$

Question 19

Which of the following is NOT a procedure that leaves the inequality symbol unchanged?

Accepted Answer

Multiplying both sides by a negative number

Question 20

If $$a \u003e 0$$, what can be said about $$\frac{1}{a}$$?

Accepted Answer

$$\frac{1}{a} \u003e 0$$

Solving Inequalities and Interval Notation in College Algebra

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