College Algebra - Final

Milestone with Answers!!

You passed this Milestone

23 questions were answered correctly.

2 questions were answered incorrectly.

1

Which of the following equations is correctly calculated?

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-2 × -7 = -14

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81 ÷ -9 = -9

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-36 ÷ 4 = 9

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4 × 12 = -48

RATIONALE

This is correct. The quotient of a positive and negative

number is always negative.

This is incorrect. The product of two negative numbers is

always positive. The correct product is 14.

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CONCEPT

Multiplying and Dividing Positive and Negative Numbers

2

Select the solution to the following system of equations:

•

•

correct

•

•

RATIONALE

This is incorrect. The quotient of a positive and a

negative number is always negative. The correct quotient

is -9.

This is incorrect. The product of two positive numbers is

always positive. The correct product is 48.

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When we add the two equations, the term will

cancel, leaving . Now we can solve for by

dividing both sides by .

Dividing by gives a solution of .

Once we divide both sides by , we get a

solution of . We can solve for by plugging

 in for in either equation.

Let's use the second equation . Once

 is plugged in for , evaluate and solve for .

Here, by multiplying by , the result

contains a term, which will cancel when

combined with the second equation. Now, we can

add the two equations together.

Before you can add equations, sometimes you

must multiply entire equations by a scalar value for

the method to work as intended. For this system,

we can multiply the second equation by .

Subtracting a negative is the same as adding a

postive . Next, subtract from both sides.

On the right side, minus equals . Now we

can solve for by dividing both sides by .

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CONCEPT

Solving a System of Linear Equations using the Addition Method

3

Perform the following operations and write the result as a single

number.

[4 + 8 × (5 – 3)] ÷ 5 + 6

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10 correct

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10.8

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2

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1.8

RATIONALE

This is the solution to the system of equations.

Following the Order of Operations, we must first

evaluate everything in parentheses and grouping

symbols. When there are brackets or braces, evaluate

the innermost operations first. Here, we must evaluate

5 minus 3 first.

5 minus 3 is 2. There are still operations inside

grouping symbols to evaluate. Multiplication comes

before addition, so we must evaluate 8 times 2 next.

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