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

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

Q: Which statement about absolute value equations is correct?

If $|u| = c$ and $c < 0$, there is no solution.

Q: Which formula is used to solve any quadratic equation $ax^2 + bx + c = 0$?

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Q: Given the quadratic equation $3x^2 - 2x + 5 = 0$, what does the discriminant tell you about the solutions?

There are two imaginary solutions.

Q: If the discriminant $b^2 - 4ac$ of a quadratic equation is zero, what can you conclude about the solutions?

There is one real (repeated) solution.

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 and $a 
eq 0$

Question 2

Solve the equation $4(2x + 1) = 29 + 3(2x - 5)$ for $x$.

Accepted Answer

$x = 5$

Question 3

Which operation does NOT generate an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 4

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

Accepted Answer

$x = 1$

Question 5

A rational equation is given by $\frac{6}{x+3} - \frac{5}{x-2} = \frac{-20}{x^2 + x - 6}$. What is the solution set?

Accepted Answer

$\{7\}$

Question 6

Solve for $q$ in the formula $\frac{1}{p} + \frac{1}{q} = \frac{1}{f}$.

Accepted Answer

$q = \frac{pf}{p-f}$

Question 7

Which statement about absolute value equations is correct?

Accepted Answer

If $|u| = c$ and $c < 0$, there is no solution.

Question 8

Solve the absolute value equation $|-2x| = 6$.

Question 9

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$ax^2 + bx + c = 0$

Question 10

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

Accepted Answer

$x = 0$ or $x = \frac{1}{2}$

Question 11

Which principle allows us to set each factor equal to zero when solving $(x-3)(x+2)=0$?

Accepted Answer

Zero-Product Principle

Question 12

Solve $x^2 + 4x = 1$ by completing the square.

Accepted Answer

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

Question 13

Which formula is used to solve any quadratic equation $ax^2 + bx + c = 0$?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Question 14

Given the quadratic equation $3x^2 - 2x + 5 = 0$, what does the discriminant tell you about the solutions?

Accepted Answer

There are two imaginary solutions.

Question 15

Which is the most efficient method to solve $x^2 - 6x = -7$?

Accepted Answer

Completing the square

Question 16

Solve the radical equation $\sqrt{x} = 6$.

Accepted Answer

$x = 36$

Question 17

A medical test uses the formula $C = 2\sqrt{t}$ to estimate the concentration $C$ of a drug in the bloodstream $t$ hours after administration. If $C = 10$, how many hours after administration is the concentration measured?

Accepted Answer

$t = 25$

Question 18

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

Accepted Answer

There is one real (repeated) solution.

Question 19

Solve the equation $|3x - 2| = 7$.

Accepted Answer

$x = 3$ or $x = -\frac{5}{3}$

Chapter P: Prerequisites – Fundamental Concepts of Algebra (P.7 Equations)

Study Guide - Practice Questions

Study Guide - Flashcards