Question 1

Which of the following is the correct solution to the linear equation $$2x + 3 = 11$$?

Accepted Answer

$$x = 4$$

Question 2

Solve the equation $$\frac{1}{2}(x + 2) = \frac{3}{4}$$ for $$x.$$

Accepted Answer

$$x = -0.5$$

Question 3

Which of the following equations is an identity?

Accepted Answer

$$2(x + 5) = 2x + 10$$

Question 4

Simplify $$i^{23}$$, where $$i is $$the imaginary unit.

Accepted Answer

$$i$$

Question 5

What is the standard form of the complex number $$2 - 3i$$?

Accepted Answer

$$2 - 3i$$

Question 6

Find the product of $$(3 + 2i)(4 - i)$$ and express your answer in standard form.

Accepted Answer

$$14 + 5i$$

Question 7

If $$a = 2$$ and $$b = -5$$, what is the conjugate of the complex number $$a + bi$$?

Accepted Answer

$$2 - 5i$$

Question 8

Divide $$\frac{3}{1 + 2i}$$ and express your answer in standard form.

Accepted Answer

$$\frac{3}{1 + 2i} = \frac{3(1 - 2i)}{(1 + 2i)(1 - 2i)} = \frac{3 - 6i}{1 + 4} = \frac{3 - 6i}{5} = 0.6 - 1.2i$$

Question 9

Which of the following is the correct quadratic equation in standard form for $$2x - 6 = 0$$?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 10

Solve the quadratic equation $$x^2 + 4x + 4 = 0$ by factoring.

Accepted Answer

$$x = -2$$

Question 11

Using the quadratic formula, solve $$x^2 - 5x + 6 = 0$.

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 12

Determine the number and type of solutions for the quadratic equation $$x^2 + 4x + 5 = 0$ using the discriminant.

Accepted Answer

Two imaginary solutions

Question 13

Express the solution set of $$x + 3 \leq 5 in $$interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 14

Solve the inequality $$2x + 12 \u003e 19$$ and express the solution in interval notation.

Accepted Answer

$$(3.5, \infty)$$

Question 15

Which of the following is a rational equation?

Accepted Answer

$$\frac{1}{x} = 12$$

Question 16

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

Accepted Answer

Question 17

Which interval notation represents the solution set for $$x \u003e -3$$?

Accepted Answer

$$(-3, \infty)$$

Question 18

If $$x^2 = -16$, what are the solutions?

Accepted Answer

$$x = 4i$$ and $$x = -4i$$

Question 19

Complete the square for $$x^2 + 6x + 5 = 0$ and solve for x$.

Accepted Answer

$$x = -1$$ and $$x = -5$$

College Algebra Study Guide: Equations and Inequalities

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