Question 1

Which of the following is the correct definition of an inequality?

Accepted Answer

A sentence with $$, $$\leq$$, or $$\geq$$ as its verb.

Question 2

Solve the inequality $$3x - 5 \leq 6 - 2x$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 3

Which principle states that if you add or subtract the same number from both sides of an inequality, the inequality remains true?

Accepted Answer

The Addition Principle for Inequalities

Question 4

What must you do when you multiply or divide both sides of an inequality by a negative number?

Accepted Answer

Reverse the inequality sign.

Question 5

Solve the compound inequality $$-3 \u003c 2x + 5 \leq 7$$ and write the solution in interval notation.

Accepted Answer

$$(-4, 1]$$

Question 6

Which of the following is a compound inequality that represents a conjunction?

Accepted Answer

$$x \u003e 2$$ and $$x \u003c 5$$

Question 7

Solve the disjunction $$2x - 5 \leq -7 or$$ $$2x - 5 \u003e 1$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, -1] \cup (3, \infty)$$

Question 8

Find the domain of the function $$f(x) = \sqrt{5 - 2x} + 1.$$

Accepted Answer

$$(-\infty, 2.5]$$

Question 9

Natalia can be paid either $$\120$ plus $$\$$10$$ per hour or $$\20$ per hour for a job that takes n$ hours. For what values of n$ is Plan B better for Natalia?

Accepted Answer

$$n \u003e 12$$

Question 10

Curt can be paid $$\1500$ per month plus a commission of 10$$\%$$ of sales, or $$\$$1150$$ per month plus a commission of $$15\% of $$sales. For what amount of monthly sales $$s is $$Plan B better than Plan A?

Accepted Answer

$$s \u003e 7000$$

Question 11

Which of the following best describes the solution set of $$x \u003e 2$$ and $$x \u003c 5$$?

Accepted Answer

$$2 \u003c x \u003c 5$$

Question 12

If $$f(x) = \frac{9}{x^2$}$$, what is the domain of $$f(x)$$?

Accepted Answer

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

Question 13

Which of the following is true about the solution set of an inequality?

Accepted Answer

It contains all values that make the inequality true.

Question 14

If $$x is a $$real number and $$a \u003c b$$, which of the following is always true?

Accepted Answer

$$a + x \u003c b + x$$

Question 15

Which of the following is a correct application of the multiplication principle for inequalities?

Accepted Answer

If $$a  0$$, then $$ac \u003c bc$$

Solving and Understanding Inequalities in College Algebra

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