Question 1

Which of the following is the 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

Which operation does NOT produce an equivalent equation when solving linear equations?

Accepted Answer

Multiplying both sides by zero

Question 3

Solve for $$x$$: $$4x + 5 = 29$$

Accepted Answer

$$x = 6$$

Question 4

Which of the following is the correct first step to solve the equation $$\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}$$?

Accepted Answer

Multiply both sides by 28, the least common denominator

Question 5

After multiplying both sides of $$\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7} by 28$$, which equation do you get?

Accepted Answer

$$28\left(\frac{x-3}{4}\right) = 28\left(\frac{5}{14}\right) - 28\left(\frac{x+5}{7}\right)$$

Question 6

Solve for $$x$$: $$\frac{x-3}{4} = \frac{5}{14} - \frac{x+5}{7}$$

Accepted Answer

$$x = 1$$

Question 7

Which of the following is a rational equation?

Accepted Answer

$$\frac{5}{x} + 2 = 7$$

Question 8

When solving a rational equation, what must you always check for before solving?

Accepted Answer

Restrictions on the variable by setting denominators equal to zero

Question 9

Solve for $$x$$: $$18\left(\frac{5}{2x}\right) = 18\left(\frac{17}{18}\right) - 18\left(\frac{1}{3x}\right)$$

Accepted Answer

$$x = 3$$

Question 10

Which of the following equations is an identity?

Accepted Answer

$$7x + 9 = 9(x + 1) - 2x$$

Question 11

Which equation is inconsistent?

Accepted Answer

$$4x - 7 = 4(x - 1) + 3$$

Question 12

A medical researcher models the average level of depression $$D in $$response to a negative life event of intensity $$x by $$the equation $$D = 10x + 53. If$$ $$D = 90$$, what is the intensity $$x$$?

Accepted Answer

$$x = 3.7$$

Question 13

Which of the following best describes a conditional equation?

Accepted Answer

An equation that is true for at least one real number

Question 14

Given $$\frac{1}{x+4} = \frac{1}{x-4}$$, what are the restricted values for $$x$$?

Accepted Answer

$$x = -4$$ and $$x = 4$$

Question 15

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

Accepted Answer

Multiplying both sides by zero

Question 16

If $$4x - 7 = 4x - 1$$, what type of equation is this?

Accepted Answer

Inconsistent equation

Question 17

Which of the following is the correct solution to $$2x = 2x + 1$$?

Accepted Answer

No solution

Question 18

A chemical reaction is modeled by $$C = 5x + 20$$, where $$C is $$the concentration and $$x is $$the time in minutes. If the concentration reaches $$C = 45$$, how many minutes have passed?

Accepted Answer

$$x = 5$$

Question 19

Which of the following equations is an example of a rational equation with a variable in the denominator?

Accepted Answer

$$\frac{2}{x} + 3 = 7$$

Chapter 1: Equations and Inequalities – Linear and Rational Equations

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