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 $$mx + b = 0$$, where $$m$$ and $$b$$ are real numbers and $$m \, 
eq \, 0.$$

Question 2

What is the solution to the equation $$\frac{3}{4}x - 1 = \frac{7}{5}$$?

Accepted Answer

$$x = \frac{16}{5}$$

Question 3

Which principle allows you to add the same number to both sides of an equation without changing the solution set?

Accepted Answer

The Addition Principle

Question 4

Solve for $$x$$: $$2(5 - 3x) = 8 - 3(x + 2).$$

Accepted Answer

$$x = \frac{8}{3}$$

Question 5

If $$-24x + 7 = 17 - 24x$$, what can you conclude about the solution set?

Accepted Answer

There is no solution.

Question 6

Solve for $$x$$: $$3 - \frac{1}{3}x = -\frac{1}{3}x + 3.$$

Accepted Answer

Any real number is a solution.

Question 7

A solar panel has a length that is $$13.6$$ inches less than twice its width. If the perimeter is $$207.4$$ inches, what is the width?

Accepted Answer

$$w = 39.1$$

Question 8

Which formula is used to calculate the distance traveled by an object moving at a constant rate?

Accepted Answer

$$d = r \cdot t$$

Question 9

A B737/800 travels at $$517$$ mph and a Saab 340B at $$290$$ mph. If the Saab leaves one hour earlier, how long after the B737/800 takes off will it overtake the Saab?

Accepted Answer

$$t \approx 1.28$$ hours

Question 10

Finley has two student loans totaling $$28,000. One loan is at 5$$\%$$ simple interest, the other at 3$$\%$$. After one year, the total interest is 1040$. How much was borrowed at 5$$\%$?

Accepted Answer

$$10,000$$

Question 11

Which of the following is the correct simple interest formula?

Accepted Answer

$$I = Prt$$

Question 12

A Central Railway freight train leaves at $$60$$ mph. One hour later, a passenger train leaves at $$80$$ mph. How long will it take the passenger train to overtake the freight train?

Accepted Answer

$$3$$ hours

Question 13

If an equation simplifies to $$3 = 3$$, what does this indicate about the solution set?

Accepted Answer

There are infinitely many solutions.

Question 14

Which of the following is NOT a step in the five-step problem-solving process?

Accepted Answer

Guess the answer and move on.

Question 15

Damarion invested $$5000$$, part at $$3\%$$ and part at $$4\%$$ simple interest. After one year, the total interest is $$176. $$Which equation represents this situation?

Accepted Answer

$$0.03x + 0.04(5000 - x) = 176$$

Question 16

If two equations have the same solution set, they are called:

Accepted Answer

Equivalent equations

Question 17

Which of the following is a correct application of the multiplication principle?

Accepted Answer

If $$a = b$$, then $$ac = bc$$ for any real number $$c.$$

Question 18

A solar panel's length is $$13.6$$ inches less than twice its width. If the width is $$39.1$$ inches, what is the length?

Accepted Answer

$$64.6$$ inches

Linear Equations, Functions, and Applications – Study Notes

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