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 $$\frac{1}{4}(x + 2) - \frac{1}{3}x = \frac{1}{12}.$$

Accepted Answer

$$x = 3$$

Question 3

Which of the following equations is an identity?

Accepted Answer

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

Question 4

Solve the rational equation $$\frac{2x + 4}{x - 1} = 5$$ and state any restrictions.

Accepted Answer

$$x = 3$$, $$x 
eq 1$$

Question 5

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

Accepted Answer

$$5i\sqrt{3}$$

Question 6

What is $$i^{22}$$?

Accepted Answer

$$-1$$

Question 7

Identify the real and imaginary parts of the complex number $$4 - 3i.$$

Accepted Answer

Real: 4, Imaginary: -3

Question 8

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

Accepted Answer

$$6 + 7i$$

Question 9

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

Accepted Answer

$$-55 + 48i$$

Question 10

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

Accepted Answer

$$a^2$$ + $$b^2$$

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 $$x^2 + x - 6 = 0$ by factoring.

Accepted Answer

$$x = -3, x = 2$$

Question 14

Solve $$2x^2 - 16 = 0$ using the square root property.

Accepted Answer

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

Question 15

Which method is best to solve $$(x + 2)^2$ = 9$$?

Accepted Answer

Square Root Property

Question 16

Determine the number and type of solutions for $$x^2 + 8x + 16 = 0$ using the discriminant.

Accepted Answer

One real solution

Question 17

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

Accepted Answer

$$(0, 5)$$

Question 18

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

Accepted Answer

$$(3.5, \infty)$$

Question 19

When solving the inequality $$-2x - 6 \leq 0$$, what must you do when dividing both sides by $$-2$$?

Accepted Answer

Reverse the inequality symbol

Precalculus Study Guide: Equations, Inequalities, and Complex Numbers

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