Q: A chemist uses the formula $$PV = nRT to $$solve for $$n$$, the number of moles of a gas. If $$P = 2$$ atm, $$V = 10 L$$, $$R = 0.082 L$$·atm/(mol·K), and $$T = 300 K$$, what is $$n$$?

$$n = \dfrac{2 \times 10}{0.082 \times 300}$$

Question 1

Which of the following best describes a linear equation in one variable?

Accepted Answer

An equation that can be written in the form $$ax + b = 0$$ where $$a 
eq 0$$

Question 2

Solve the following linear equation for $$x$$: $$6(3x - 1) = 8 - (10x - 14)$$

Accepted Answer

$$x = 0.5$$

Question 3

Which of the following is an example of a conditional equation?

Accepted Answer

$$2x = 8$$

Question 4

A contradiction in algebra is best described as:

Accepted Answer

An equation that is never true for any value of the variable

Question 5

Solve for $$x$$: $$0.04(x - 12) + 0.06x = 1.52$$

Accepted Answer

$$x = 20$$

Question 6

Which of the following is NOT a linear equation?

Accepted Answer

$$x^2 + 2x = 5$

Question 7

Solve for $$x$$: $$\dfrac{2x + 4}{3} + \dfrac{1}{2} = \dfrac{1}{4}x - \dfrac{7}{3}$$

Accepted Answer

$$x = -4$$

Question 8

Which of the following statements about identities is correct?

Accepted Answer

An identity is true for all values of the variable

Question 9

Solve for $$x$$: $$\dfrac{1}{14}(3x - 2) = \dfrac{x + 10}{10}$$

Accepted Answer

$$x = 8$$

Question 10

Which of the following is a literal equation?

Accepted Answer

$$I = Prt$$

Question 11

Solve for $$t in $$the formula $$I = Prt.$$

Accepted Answer

$$t = \dfrac{I}{Pr}$$

Question 12

Given the formula $$A - P = Prt$$, solve for $$P.$$

Accepted Answer

$$P = \dfrac{A}{1 + rt}$$

Question 13

Which of the following is the correct solution for $$x in$$ $$3(2x - 5a) + 4b = 4x - 2$$?

Accepted Answer

$$x = \dfrac{6a + 4b + 2}{4 - 6}$$

Question 14

Solve for $$h in $$the formula $$S = 2lw + 2wh + 2hl.$$

Accepted Answer

$$h = \dfrac{S - 2lw}{2w + 2l}$$

Question 15

Which of the following is a real-world example of a literal equation?

Accepted Answer

The equation for the area of a rectangle: $$A = lw$$

Question 16

Which of the following is the solution set for the equation $$x + 2 = x + 3$$?

Accepted Answer

No solution

Question 17

Which of the following is true about the solution set of an identity?

Accepted Answer

It contains all real numbers

Question 18

A medical researcher uses the formula $$C = \dfrac{A}{B} to $$calculate the concentration of a drug in the bloodstream, where $$A is $$the amount of drug and $$B is $$the blood volume. If $$A = 50 mg $$and $$B = 2 L$$, what is the concentration $$C$$?

Accepted Answer

$$C = 25 mg/L$$

Question 19

A chemist uses the formula $$PV = nRT to $$solve for $$n$$, the number of moles of a gas. If $$P = 2$$ atm, $$V = 10 L$$, $$R = 0.082 L$$·atm/(mol·K), and $$T = 300 K$$, what is $$n$$?

Accepted Answer

$$n = \dfrac{2 	imes 10}{0.082 	imes 300}$$

Equations and Linear Equations: Basic Terminology and Methods

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