Question 1

Which of the following is the general form of a linear equation in one variable?

Accepted Answer

$$ax + b = 0$$

Question 2

What is the solution to the equation $$3x - 7 = 2x + 5$$?

Accepted Answer

$$x = 12$$

Question 3

Solve the equation $$\frac{2x}{5} - 3 = 1.$$

Accepted Answer

$$x = 10$$

Question 4

Which operation does NOT generate an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 5

Solve the rational equation $$\frac{3}{x} = 6$$ for $$x.$$

Accepted Answer

Question 6

Which of the following equations is an identity?

Accepted Answer

$$2(x + 3) = 2x + 6$$

Question 7

A rational equation has a variable in the denominator. What must you always check for before solving?

Accepted Answer

Values that make the denominator zero

Question 8

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

Accepted Answer

Question 9

Which of the following best describes an inconsistent equation?

Accepted Answer

An equation with no solution

Question 10

A mathematical model for depression is $$D = 2.7x + 0. If a $$person has a depression level $$D = 10$$, what is the intensity $$x of $$the negative life event?

Accepted Answer

$$x = 3.7$$

Question 11

Which of the following is NOT a valid step in solving a linear equation?

Accepted Answer

Multiplying both sides by zero

Question 12

Solve the equation $$\frac{5}{x-2} = 1$$ for $$x.$$

Accepted Answer

$$x = 7$$

Question 13

Which of the following equations is conditional?

Accepted Answer

$$x + 2 = 5$$

Question 14

If $$y_1$$ = \frac{2}{x-4}$$ and y_2$ = \frac{3}{x+4}$$, for which value of $$x$$ are $$y_1$$ = $$y_2$$?

Accepted Answer

$$x = 11$$

Question 15

Which of the following is a valid equivalent equation to $$2x + 3 = 7$$?

Accepted Answer

$$2x = 4$$

Question 16

Solve the equation $$\frac{4}{x} = 2$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 17

Which of the following is an example of a real-world application of a linear equation?

Accepted Answer

Calculating the intensity of a negative life event given a depression score

Chapter 1.2: Linear Equations and Rational Equations - College Algebra Study Notes

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