Question 1

Which of the following is the correct definition of a 'real number'?

Accepted Answer

A number that is either rational or irrational, including all numbers on the number line.

Question 2

What is the solution to the equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 3

A medical researcher records the temperature of a patient as $$T = 98.6$$ degrees Fahrenheit. Which property of real numbers is illustrated when she adds $$0 to $$the temperature and gets the same value?

Accepted Answer

Additive Identity

Question 4

Simplify the expression $$3(2x - 4) + 5x.$$

Accepted Answer

$$11x - 12$$

Question 5

Translate the phrase 'the sum of twice a number and five' into an algebraic expression.

Accepted Answer

$$2x + 5$$

Question 6

A chemical reaction requires the temperature to be above $$50^	ext{o}C. $$Which interval notation represents all possible temperatures for this reaction?

Accepted Answer

$$(50, \infty)$$

Question 7

Solve the compound inequality $$-3 \u003c 2x + 1 \leq 7.$$

Accepted Answer

$$-2 \u003c x \leq 3$$

Question 8

Which of the following is the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13)$$?

Accepted Answer

$$2$$

Question 9

A business tracks its profit using the equation $$P = 3x + 200$$, where $$x is $$the number of units sold. What is the $$y-$$intercept of this equation?

Accepted Answer

$$200$$

Question 10

Which equation represents a line that is perpendicular to $$y = 2x + 1$$?

Accepted Answer

$$y = -\frac{1}{2}x + 4$$

Question 11

Solve the system of equations: $$x + y = 10$$ and $$x - y = 2.$$

Accepted Answer

$$x = 6, y = 4$$

Question 12

A hospital uses the formula $$C = 50n + 200 to $$calculate the cost $$C$$ for $$n$$ patients. If the total cost is $$450$$, how many patients were treated?

Accepted Answer

$$n = 4$$

Question 13

Which of the following is the equation of a horizontal line passing through $$(3, -2)$$?

Accepted Answer

$$y = -2$$

Question 14

If a line has a slope of $$0$$, which statement is true?

Accepted Answer

The line is horizontal.

Question 15

Solve for $$y in $$the equation $$3x + 2y = 12.$$

Accepted Answer

$$y = 6 - \frac{3}{2}x$$

Question 16

A company wants to graph the inequality $$y \u003e 2x - 1. $$Which region should be shaded?

Accepted Answer

Above the line $$y = 2x - 1$$

Question 17

Which of the following is the solution set for the inequality $$4x - 7 \u003c 9$$?

Accepted Answer

$$x \u003c 4$$

Question 18

A student solves the system $$2x + 3y = 12$$ and $$x - y = 1$$ using the substitution method. What is the value of $$y$$?

Accepted Answer

$$y = 3$$

Question 19

Which property of real numbers is used in the equation $$a(b + c) = ab + ac$$?

Accepted Answer

Distributive Property

Question 20

A car rental company charges a flat fee of $$25$$ plus $$0.15$$ per mile driven. Write the equation for the total cost $$C if$$ $$m$$ miles are driven, and find the cost for $$120$$ miles.

Accepted Answer

$$C = 25 + 0.15m; C = 43$$

Elementary Algebra Syllabus and Study Guide: Foundations for College Algebra

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