Question 1

Which of the following is the correct first step to solve the equation $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

Distribute the 3 to both terms inside the parentheses

Question 2

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

Accepted Answer

$$x = -6$$

Question 3

Which of the following equations is an identity?

Accepted Answer

$$x + 5 = x + 2 + 3$$

Question 4

What is the restriction for the rational equation $$\frac{x}{x-1} = 7$$?

Accepted Answer

$$x 
eq 1$$

Question 5

Simplify $$\sqrt{-75}.$$

Accepted Answer

$$5i\sqrt{3}$$

Question 6

What is $$i^{85}$$?

Accepted Answer

$$-i$$

Question 7

Identify the real and imaginary parts of the complex number $$4 - 9i.$$

Accepted Answer

Real part: 4, Imaginary part: -9

Question 8

Find the sum $$(4 + 8i) + (2 + 3i)$$ and express your answer in standard form.

Accepted Answer

$$6 + 11i$$

Question 9

Multiply $$(3 + 8i)(2 - 3i)$$ and express your answer in standard form.

Accepted Answer

$$30 - 7i$$

Question 10

What is the product of a complex number and its conjugate, $$(a + bi)(a - bi)$$?

Accepted Answer

$$a^2$$ + $$b^2 ($$since $$i^2 = -1$)

Question 11

Divide $$\frac{6 + i}{4 - 2i}$$ and express your answer in standard form.

Accepted Answer

$$1 + \frac{2}{5}i$$

Question 12

Write $$-4x^2 + x = 8$ in standard quadratic form and identify a$, b$, and c$.

Accepted Answer

$$a = -4, b = 1, c = -8$$

Question 13

Solve the quadratic equation $$2x^2 + 7x + 6 = 0$ by factoring.

Accepted Answer

$$x = -2, x = -1$$

Question 14

Using the square root property, solve $$(x - 2)^2$ = 5.$$

Accepted Answer

$$x = 2 \pm \sqrt{5}$$

Question 15

Solve $$x^2 + 6x + 1 = 0$ by completing the square.

Accepted Answer

$$x = -3 \pm 2\sqrt{2}$$

Question 16

Use the quadratic formula to solve $$3x^2 + 4x + 1 = 0$.

Accepted Answer

$$x = \frac{-4 \pm 2}{6}$$

Question 17

For the quadratic equation $$x^2 - 10x + 25 = 0$, what is the value of the discriminant and how many real solutions does it have?

Accepted Answer

Discriminant = 0, one real solution

Question 18

Express the set $$\{x | 0 \u003c x \u003c 5\} in $$interval notation.

Accepted Answer

$$(0, 5)$$

Question 19

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

Accepted Answer

$$(3.5, \infty)$$

Question 20

If you multiply or divide both sides of an inequality by a negative number, what must you do to the inequality symbol?

Accepted Answer

Reverse the direction of the inequality symbol

Equations & Inequalities: College Algebra Study Guide

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