Question 1

Which of the following represents the interval notation for all real numbers x such that $$-2 \u003c x \leq 5$$?

Accepted Answer

$$( -2, 5 ]$$

Question 2

Given the inequality $$3x - 7 \u003c 8$$, which of the following is the solution set in interval notation?

Accepted Answer

$$( -\infty, 5 )$$

Question 3

If $$x \u003e -4$$, which of the following is the correct interval notation?

Accepted Answer

$$( -4, \infty )$$

Question 4

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

Accepted Answer

$$( -\infty, 2 ]$$

Question 5

Which property of inequalities justifies the following step: If $$a \u003c b$$, then $$a + c \u003c b + c$$?

Accepted Answer

Addition Property of Inequalities

Question 6

If $$x \u003c 3$$ and both sides are multiplied by $$-2$$, what is the resulting inequality?

Accepted Answer

$$-2x \u003e -6$$

Question 7

Which of the following intervals represents all real numbers?

Accepted Answer

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

Question 8

Solve the combined inequality $$2 \u003c 3x + 1 \leq 10$$ and write the solution in interval notation.

Accepted Answer

$$( \frac{1}{3}, 3 ]$$

Question 9

A chemical process requires the temperature $$T to be $$between $$20^\circC $$and $$80^\circC$$, inclusive. Express this requirement in interval notation.

Accepted Answer

$$[ 20, 80 ]$$

Question 10

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 11

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

Accepted Answer

$$( -1, \infty )$$

Question 12

A hospital’s generator is rated at a resistance of $$20$$ ohms. If the voltage varies from $$220 to$$ $$240$$ volts, inclusive, what is the range of current (in amperes) the generator will draw? (Use Ohm’s Law: $$E = IR)$$

Accepted Answer

$$[ 11, 12 ]$$

Question 13

Which of the following is the correct inequality notation for the interval $$[ 0, 3 )$$?

Accepted Answer

$$0 \leq x \u003c 3$$

Question 14

If $$x \leq -5$$, which interval notation correctly represents the solution set?

Accepted Answer

$$( -\infty, -5 ]$$

Question 15

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

Accepted Answer

$$[ 5, \infty )$$

Question 16

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

Accepted Answer

Multiplying both sides by a negative number

Question 17

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

Accepted Answer

$$( 1, 4 )$$

Question 18

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

Accepted Answer

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

Question 19

Which of the following is the correct solution set for the inequality $$-x \u003e 7$$?

Accepted Answer

$$x \u003c -7$$

Question 20

A medication is effective only if the patient’s temperature $$T$$ satisfies $$36 \u003c T \u003c 38. $$Which interval notation represents this range?

Accepted Answer

$$( 36, 38 )$$

Chapter 1.5: Solving Inequalities – College Algebra Study Guide

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