Question 1

Which of the following equations is a linear equation?

Accepted Answer

$$2x + 5 = 9$$

Question 2

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

Accepted Answer

Question 3

Which of the following is the correct solution set for the inequality $$2x - 5 \u003c 9 in $$interval notation?

Accepted Answer

$$(-\infty, 7)$$

Question 4

A rational equation is given by $$\frac{1}{x} = 12. $$What is the solution, and what restriction must be considered?

Accepted Answer

Question 5

Simplify $$\sqrt{-16}$$ using the imaginary unit.

Accepted Answer

$$4i$$

Question 6

What is $$i^7$$?

Accepted Answer

$$-i$$

Question 7

Write the complex number $$3 - 4i in $$standard form and identify its real and imaginary parts.

Accepted Answer

Real part: $$3$$, Imaginary part: $$-4$$

Question 8

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

Accepted Answer

Question 9

What is the conjugate of the complex number $$5 - 2i$$?

Accepted Answer

$$5 + 2i$$

Question 10

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

Accepted Answer

$$\frac{3(1 - 2i)}{5}$$

Question 11

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

Accepted Answer

Question 12

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

Accepted Answer

$$x = -2$$

Question 13

Use the square root property to solve $$x^2 = 25$.

Accepted Answer

$$x = \pm 5$$

Question 14

Solve $$x^2 + 1 = 0$ using the square root property. What type of roots does this equation have?

Accepted Answer

Two imaginary roots

Question 15

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

Accepted Answer

$$x = -1, x = -5$$

Question 16

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

Accepted Answer

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

Question 17

Given the quadratic equation $$x^2 + 2x + 5 = 0$, use the discriminant to determine the number and type of solutions.

Accepted Answer

Two imaginary solutions

Question 18

Express the solution set of $$x \u003e -3 in $$interval notation.

Accepted Answer

$$(-3, \infty)$$

Question 19

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

Accepted Answer

$$(3.5, \infty)$$

Question 20

A chemical reaction requires the temperature $$T to $$satisfy $$\frac{1}{2}(T + 1) \geq 2(T + 2). $$What is the solution set for $$T in $$interval notation?

Accepted Answer

$$(-\infty, -3)$$

Precalculus Study Notes: Equations and Inequalities (Ch. 1)

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