Question 1

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

Accepted Answer

$$2x + 5 = 11$$

Question 2

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

Accepted Answer

$$x = 11$$

Question 3

Solve the equation $$\dfrac{2x}{7} + \dfrac{3}{2} = 5.$$

Accepted Answer

$$x = 11.375$$

Question 4

Which operation does NOT generate an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 5

Solve the rational equation $$\dfrac{1}{x} + \dfrac{2}{3} = 1$$ for $$x ($$excluding restricted values).

Accepted Answer

$$x = 6$$

Question 6

Which of the following equations is an identity?

Accepted Answer

$$2x + 3 = 2x + 3$$

Question 7

A rational equation has the form $$\dfrac{2}{x-4} = \dfrac{3}{x+4}. $$What are the restricted values for $$x$$?

Accepted Answer

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

Question 8

Solve and categorize the equation $$2(x + 3) = 2x + 6.$$

Accepted Answer

Identity

Question 9

Which of the following best describes an inconsistent equation?

Accepted Answer

An equation that is not true for any real number

Question 10

A chemist mixes two solutions, one with a concentration of $$x$$ grams per liter and another with $$2x$$ grams per liter, to obtain a total of $$15$$ liters of a $$1.5x$$ grams per liter solution. Which equation models this scenario?

Accepted Answer

$$x + 2x = 15 	imes 1.5$$

Question 11

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

Accepted Answer

$$x = 2$$

Question 12

Which of the following is a conditional equation?

Accepted Answer

$$2x = 10$$

Question 13

If $$\dfrac{1}{x} + \dfrac{1}{x-2} = 1$$, what is the least common denominator (LCD) you should use to clear the fractions?

Accepted Answer

$$x(x-2)$$

Question 14

A medical researcher is modeling the spread of a virus using the equation $$\dfrac{N}{t} = 5$$, where $$N is $$the number of cases and $$t is $$time in days. If there are $$100$$ cases, how many days has the virus been spreading?

Accepted Answer

$$t = 20$$

Question 15

Solve the equation $$\dfrac{2}{x} + 3 = 5$$ for $$x.$$

Accepted Answer

Question 16

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

Accepted Answer

Multiply both sides by zero

Question 17

If $$\dfrac{1}{x} = 0$$, what is the solution for $$x$$?

Accepted Answer

No solution

Question 18

A car rental company charges a flat fee of $$\50$ plus $$\$$0.20$$ per mile driven. If the total cost is $$\90$, how many miles were driven?

Accepted Answer

$$200$$

Question 19

Which of the following equations is inconsistent?

Accepted Answer

$$x + 2 = x + 3$$

Question 20

Solve the equation $$\dfrac{2x}{5} = 8$$ for $$x.$$

Accepted Answer

$$x = 20$$

Chapter 1: Equations and Inequalities – Linear and Rational Equations

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