Question 1

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

Accepted Answer

$$ax + b = 0$$, where $$a$$ and $$b$$ are real numbers, $$a 
eq 0$$

Question 2

What is the solution to the equation $$4(2x+1) = 29 + 3(2x-5)$$?

Accepted Answer

$$x = 5$$

Question 3

Which operation does NOT generate an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 4

Solve for $$x in $$the equation $$\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}.$$

Accepted Answer

$$x = 11$$

Question 5

Which of the following is a rational equation?

Accepted Answer

$$\frac{x-3}{x+2} = 5$$

Question 6

Given the quadratic equation $$2x^2 + x - 6 = 0$, what are the possible values of x$?

Accepted Answer

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

Question 7

What is the solution set for the absolute value equation $$|1-2x| = 5$$?

Accepted Answer

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

Question 8

Which property allows you to solve $$u^2 = d$ by writing u$$ = \pm \sqrt{d}$$?

Accepted Answer

Square root property

Question 9

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude?

Accepted Answer

There are two imaginary solutions

Question 10

Solve the radical equation $$\sqrt{x+3} + 3 = x$$ and identify any extraneous solutions.

Accepted Answer

$$x = 6 is $$the only solution

Question 11

Which method is most efficient for solving $$x^2 - 4 = 0$?

Accepted Answer

Factoring

Question 12

Given the formula $$af + pf = pa$$, solve for $$f in $$terms of $$a$$ and $$p.$$

Accepted Answer

$$f = \frac{a(p-r)}{p}$$

Question 13

Which of the following equations is quadratic?

Accepted Answer

$$x^2 + 3x + 2 = 0$

Question 14

What is the solution to $$3x^2 - 21 = 0$ using the square root property?

Accepted Answer

$$x = \pm \sqrt{7}$$

Question 15

If $$b^2 - 4ac = 0$ for a quadratic equation, what does this indicate about the solutions?

Accepted Answer

There is one real repeated solution

Question 16

Which step is necessary when solving a radical equation such as $$\sqrt{x+3} = x-3$$?

Accepted Answer

Isolate the radical and raise both sides to the nth power

Question 17

What is the zero-product principle used for?

Accepted Answer

Solving quadratic equations by factoring

Question 18

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 19

A quadratic equation $$3x^2 - 2x + 5 = 0$ has what type of solutions?

Accepted Answer

Two imaginary solutions

Question 20

Which of the following is a necessary step when checking solutions to radical equations?

Accepted Answer

Substitute the solution back into the original equation to check for extraneous solutions

Precalculus Chapter P.7: Equations – Fundamental Concepts of Algebra

Study Guide - Practice Questions