Question 1

Which of the following best defines a 'solution set' for an equation?

Accepted Answer

All the numbers that make the equation a true statement.

Question 2

What is the first step when solving a linear equation according to the provided steps?

Accepted Answer

List any restrictions on the variable.

Question 3

Solve for $$x$$: $$3x - 5 = 4$$

Accepted Answer

$$x = 3$$

Question 4

Which of the following equations has no solution?

Accepted Answer

$$\dfrac{3x}{x-1} + 2 = \dfrac{3}{x-1}$$

Question 5

What is the least common denominator (LCD) of the fractions in the equation $$\dfrac{1}{2}(x+5) - 4 = \dfrac{1}{3}(2x-1)$$?

Accepted Answer

$$6$$

Question 6

Solve for $$x$$: $$6(x-1) + 4 = 3(7x+1)$$

Accepted Answer

$$x = -\dfrac{2}{5}$$

Question 7

Which step is necessary when solving an equation with fractions?

Accepted Answer

Multiply both sides by the least common denominator of all fractions.

Question 8

A chemist needs to prepare a solution by mixing two liquids. She has 100 mL of a 30% solution and wants to add pure solvent to dilute it to a 20% solution. How much pure solvent should she add?

Accepted Answer

$$50 mL$$

Question 9

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

Accepted Answer

Divide both sides by zero to eliminate the variable.

Question 10

Andy grossed $435 one week by working 52 hours. His employer pays time-and-a-half for all hours worked in excess of 40 hours. What is Andy’s hourly wage?

Accepted Answer

$$7.50$$

Question 11

Solve for $$x$$: $$\dfrac{1}{2}(x+5) - 4 = \dfrac{1}{3}(2x-1)$$

Accepted Answer

$$x = 5$$

Question 12

If an equation is written in the form $$ax + b = 0$$ where $$a 
eq 0$$, what is the solution for $$x$$?

Accepted Answer

$$x = -\dfrac{b}{a}$$

Question 13

A medical researcher is testing a new drug. She needs to prepare 200 mL of a 15% saline solution by mixing a 10% solution and a 25% solution. How many mL of the 25% solution should she use?

Accepted Answer

$$66.67 mL$$

Question 14

Which of the following best describes the process of 'checking your solution' in solving equations?

Accepted Answer

Substitute your solution back into the original equation to verify it makes the equation true.

Question 15

Solve for $$x$$: $$2x + 5 = 9$$

Accepted Answer

$$x = 2$$

Question 16

A student claims that the solution to $$\dfrac{3x}{x-1} + 2 = \dfrac{3}{x-1} is$$ $$x = 2. Is $$this correct?

Accepted Answer

No, because substituting $$x = 2$$ does not satisfy the equation.

Question 17

Which of the following is a restriction on the variable for the equation $$\dfrac{1}{x-3} = 2$$?

Accepted Answer

$$x 
eq 3$$

Question 18

A historical event occurred in the year $$x. If $$the sum of the digits of $$x is 15 $$and $$x is $$between 1900 and 2000, which of the following could be the year?

Accepted Answer

1968

Question 19

Which of the following is the correct order of steps to solve a linear equation with fractions?

Accepted Answer

List restrictions, clear fractions, remove parentheses, collect variable terms, simplify and solve, check solution.

Solving Linear Equations and Applications in Precalculus

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