Question 1

Which of the following is the correct definition of a linear equation in one variable?

Accepted Answer

An equation that can be written in the form $$ax + b = 0$$, with $$a 
eq 0.$$

Question 2

Solve the equation $$2x - 3 = 3x + 5. $$What is the value of $$x$$?

Accepted Answer

$$x = -8$$

Question 3

A rational equation is an equation that contains:

Accepted Answer

Variables in the denominator

Question 4

Solve the rational equation $$\frac{2x}{3} = \frac{5}{6}.$$

Accepted Answer

$$x = \frac{5}{4}$$

Question 5

Which of the following is the correct solution to the quadratic equation $$x^2 - 4x + 3 = 0$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 6

A company’s cost function is $$C(x) = 1285x + 24943. $$What is the cost when $$x = 30$$?

Accepted Answer

$$C(30) = 38,843$$

Question 7

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 8

What is the result of multiplying $$(2 + 3i)(1 - 4i)$$?

Accepted Answer

$$14 - 5i$$

Question 9

Solve the quadratic equation $$x^2 = 9$ using the square root property.

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 10

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 11

If $$x is a $$solution to $$\frac{5}{2x} = \frac{3}{4}$$, what is the value of $$x$$?

Accepted Answer

$$x = \frac{10}{3}$$

Question 12

Which of the following best describes the solution set for the inequality $$x \u003e 2$$?

Accepted Answer

$$(2, \infty)$$

Question 13

A ladder is leaning against a building. If the ladder is 35 ft long and the base is 10 ft from the building, how high up the wall does the ladder reach? (Use the Pythagorean Theorem.)

Accepted Answer

$$\sqrt{35^2$ - 10^2$} = \sqrt{1225 - 100} = \sqrt{1125} \approx 33.54 ft$$

Question 14

Which of the following is the correct solution to $$3x + 5 = 2x - 7$$?

Accepted Answer

$$x = -12$$

Question 15

If $$x = 2 is a $$solution to the equation $$ax + b = 0$$, what is the value of $$a if$$ $$b = -6$$?

Accepted Answer

$$a = 3$$

Question 16

Which of the following is the correct result of dividing $$\frac{8 - 12i}{5 + 12i}$$ and writing the answer in standard form?

Accepted Answer

$$\frac{8 - 12i}{5 + 12i} = \frac{-40 - 96}{25 + 144} + \frac{60 - 80}{25 + 144}i = \frac{-40}{169} + \frac{-80}{169}i$$

College Algebra Study Guide: Linear, Rational, Quadratic Equations, Complex Numbers, and Inequalities

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