Q: Which of the following correctly represents the order of operations for evaluating an expression?

$$\text{Parentheses} \rightarrow \text{Exponents} \rightarrow \text{Multiplication/Division} \rightarrow \text{Addition/Subtraction}$$

Q: Which of the following demonstrates the distributive property correctly?

$$5(13 - 6) = 5 \times 13 - 5 \times 6$$

Question 1

Which of the following correctly represents the order of operations for evaluating an expression?

Accepted Answer

$$	ext{Parentheses} ightarrow 	ext{Exponents} ightarrow 	ext{Multiplication/Division} ightarrow 	ext{Addition/Subtraction}$$

Question 2

Evaluate the following expression using the correct order of operations: $$2 + 4 	imes 3^2$ - (9 \div 3)$$

Accepted Answer

$$29$$

Question 3

What is the result of $$-(-(-2))$$?

Accepted Answer

$$-2$$

Question 4

A chemist is mixing two solutions: one with a temperature of $$-5^\circC $$and another with $$13^\circC. If $$the final temperature is the sum of the two, what is the result?

Accepted Answer

$$8^\circC$$

Question 5

Which of the following demonstrates the distributive property correctly?

Accepted Answer

$$5(13 - 6) = 5 	imes 13 - 5 	imes 6$$

Question 6

Solve for $$x in $$the equation $$2x + 3 = 11.$$

Accepted Answer

$$x = 4$$

Question 7

A medical researcher is tracking a patient’s weight change. If the patient lost $$17$$ pounds and then gained $$11$$ pounds, what is the net change?

Accepted Answer

$$-6$$ pounds

Question 8

Which step is NOT part of the equation solving process described in the notes?

Accepted Answer

Guessing

Question 9

Solve for $$y in $$the equation $$-5y - 7 = 63.$$

Accepted Answer

$$y = -14$$

Question 10

Which of the following is the correct simplification of $$-6(2x - 3y)$$?

Accepted Answer

$$-12x + 18y$$

Question 11

A business lost $$3,000$$ dollars in January and $$9,000$$ dollars in February. What is the total loss?

Accepted Answer

$$-12,000$$

Question 12

If $$-(-a) = a$$, what is the value of $$-(-(-5))$$?

Accepted Answer

$$-5$$

Question 13

Solve for $$x in $$the equation $$\dfrac{3x}{4} = 7.$$

Accepted Answer

$$x = \dfrac{28}{3}$$

Question 14

Which of the following is true about the sum of a positive and a negative number?

Accepted Answer

The sign of the result is the sign of the number with the greater absolute value.

Question 15

A physics problem involves the expression $$2(7^2) - 4 + 24$$ \div 3$$. What is the value?

Accepted Answer

$$94$$

Question 16

Which property allows you to solve $$2x + 3 = 11 by $$subtracting $$3$$ from both sides?

Accepted Answer

Balance

Question 17

Solve for $$x in $$the equation $$-2(3x - 7) = 4(6x + 11).$$

Accepted Answer

$$x = -1$$

Question 18

A real estate agent calculates commission as $$5\% of $$the sale price. If the sale price is $$\240$$,000$, what is the commission?

Accepted Answer

$$\12$$,000$

Question 19

Which of the following is the correct simplification of $$5(-6)$$?

Accepted Answer

$$-30$$

Question 20

A student claims that $$-5 + 13 = -18. $$What is the error in this calculation?

Accepted Answer

They added the numbers without considering the sign; the correct answer is $$8.$$

Equation Solving Principles and Order of Operations in College Algebra

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