1.
Brett was given the problem: “Evaluate + 5 when x = 3.” Brett wrote that the answer was 41. Was Brett correct? Explain your answer.
2.
The Excel Cable Company has a monthly fee of $32.00 and an additional charge of $8.00 for each premium channel. The Best Cable Company has a monthly fee of $26.00 and an additional charge of 10.00 for each premium channel. The Horton family is deciding which of these two cable companies to subscribe to. a. Write an equation that represents the cost of each cable company’s monthly fee. Let c = cost b. For what number of premium channels will the total monthly subscription fee for the Excel and Best Cable companies be the same? c. The Horton family decides to subscribe to 2 premium channels for a period of one year. (1) Which cable company should they subscribe to in order to spend less money? (2) How much money will the Hortons save in one year by using the less expensive company?
3.
Each student takes eight classes and has a separate notebook for each class.- Determine the number of student notebooks in the school, given the number of students.
Number of StudentsNumber of Notebooks225 300 410 520 - Write an expression that represents the number of notebooks in the school, if the number of students is “x”.
- What would be the expression from part b if each student used their notebooks for 2 classes, instead of having a separate notebook for each class?
4.
Identify the algebraic expression with a coefficient of 3 and a constant of -5.
Correct Answer
D. 3x-5
Explanation
The given expression, 3x-5, has a coefficient of 3 because the variable x is multiplied by 3. The constant term is -5 because it is a number that does not have a variable attached to it. Therefore, the expression matches the criteria of having a coefficient of 3 and a constant of -5.
5.
Translate the verbal phrases into algebraic expressions. Three times the difference of eight and a number x.
Correct Answer
A. 3(8 â€“ x)
Explanation
The given verbal phrase "Three times the difference of eight and a number x" can be translated into the algebraic expression 3(8 â€“ x). This expression represents three times the difference between eight and the number x.
6.
Twelve decreased by the quantity five times a number y.
Correct Answer
C. 12 â€“ 5y
Explanation
The given expression states that twelve is decreased by the quantity five times a number y. This can be represented as 12 - 5y, where 5y represents five times the number y and subtracting it from twelve gives the final result. Therefore, the correct answer is 12 - 5y.
7.
Which expression represents “5 less than the product of 7 and x”?
Correct Answer
B. 7x â€“ 5
Explanation
The expression "7x - 5" represents "5 less than the product of 7 and x". This can be understood by breaking down the expression. The product of 7 and x is represented by 7x, and when we subtract 5 from it, we get "5 less than the product of 7 and x". Therefore, the correct answer is 7x - 5.
8.
Evaluate the expression.-8x when x = 3
Correct Answer
C. -24
Explanation
The given expression is -8 multiplied by 3. When we multiply -8 and 3, we get -24. Therefore, the correct answer is -24.
9.
4x^{2 } - 2x when x = 3
Correct Answer
A. 30
Explanation
The given expression is 4x2 - 2x. When x is substituted with 3, the expression becomes 4(3)^2 - 2(3), which simplifies to 4(9) - 6 = 36 - 6 = 30. Therefore, the answer is 30.
10.
5(x + 9) when x = 5
Correct Answer
C. 70
Explanation
When we substitute x with 5 in the expression 5(x + 9), we get 5(5 + 9). Simplifying this further, we have 5(14), which equals 70. Therefore, the correct answer is 70.
11.
when x = 2
Correct Answer
A. 4.5
Explanation
When x = 2, the given options are 4.5, 2.5, 4, and 2. Since the answer is given as 4.5, it suggests that when x is equal to 2, the correct value is 4.5.
12.
Identify the like term(s) for 8x.
Correct Answer(s)
A. X
C. 16x
Explanation
The like terms for 8x are x and 16x because they both have the same variable, which is x. The coefficients (8 and 16) can be different, but as long as the variables are the same, they are considered like terms.
13.
Use the distributive property to rewrite the expression without parentheses. 5(x – 3)
Correct Answer
D. 5x-15
Explanation
The given expression, 5(x â€“ 3), can be rewritten using the distributive property as 5x â€“ 15.
14.
(x + 2)4
Correct Answer
C. 4x+8
Explanation
The given expression is (x + 2)4. To simplify this expression, we need to distribute the 4 to both terms inside the parentheses. Distributing the 4 gives us 4x + 8. Therefore, the correct answer is 4x + 8.
15.
Collect like terms. 7x + 8x + x + 3
Correct Answer
C. 16x + 3
Explanation
To collect like terms, we combine the terms with the same variable. In this expression, we have three terms with the variable x: 7x, 8x, and x. We can add these terms together to get 16x. The constant term 3 remains unchanged. Therefore, the correct answer is 16x + 3.
16.
6x^{2 }+ 3x + x^{2 } + 7x – 5
Correct Answer
D. 7x^2 + 10x â€“ 5
Explanation
The given expression is a polynomial. To simplify it, we can combine like terms. First, we combine the terms with the same degree of x, which are 6x^2 and x^2. This gives us 7x^2. Then, we combine the terms with x, which are 3x, 7x, and 10x. This gives us 20x. Finally, we combine the constant terms, which are -5. Therefore, the simplified expression is 7x^2 + 20x - 5.
17.
5(x – 3) + 8x
Correct Answer
B. 13x - 15
Explanation
The given expression is 5(x - 3) + 8x. By distributing the 5 to both terms inside the parentheses, we get 5x - 15. Adding this to 8x gives us 13x - 15.
18.
Name the inverse operation used to solve this equation: x + 12 = -27
Correct Answer
D. Subtraction
Explanation
To solve the equation x + 12 = -27, we need to isolate the variable x. The inverse operation of addition is subtraction, so by subtracting 12 from both sides of the equation, we can eliminate the 12 on the left side and simplify the equation to x = -39. Therefore, the correct answer is subtraction.
19.
Name the inverse operation used to solve this equation: -3m = -27
Correct Answer
B. Division
Explanation
To solve the equation -3m = -27, we need to find the value of m. The inverse operation used to isolate the variable m is division. By dividing both sides of the equation by -3, we can cancel out the coefficient of m and find that m = 9. Division is the inverse operation of multiplication, so dividing both sides of the equation by -3 allows us to solve for m.
20.
Solve the equation: 1 – 10x = 81
Correct Answer
B. -8
Explanation
To solve the equation 1 - 10x = 81, we want to isolate the variable x. First, we subtract 1 from both sides of the equation to get -10x = 80. Then, we divide both sides by -10 to solve for x. Therefore, the correct answer is -8.
21.
- Solve the equation: p + 7 = -23
Correct Answer
B. 36
Explanation
To solve the equation p + 7 = -23, we need to isolate the variable p. We can do this by subtracting 7 from both sides of the equation. This gives us p = -23 - 7, which simplifies to p = -30. However, none of the answer choices match this solution. Therefore, the correct answer is not available.
22.
Solve the equation: 1.9k – 3 – 7.5k = 4
Correct Answer
B. -1.25
Explanation
To solve the equation, we need to combine like terms. First, we can combine the terms with k: 1.9k - 7.5k = -5.6k. Then, we can combine the constant terms: -3 - 4 = -7. Finally, we have -5.6k - 7 = 4. To isolate k, we can add 7 to both sides: -5.6k = 11. Dividing both sides by -5.6 gives us k = -1.25. Therefore, the correct answer is -1.25.
23.
Solve the equation: –6(4d + 10) + 7d = -2d
Correct Answer
D. -4
Explanation
To solve the equation, we need to simplify and combine like terms. First, distribute -6 to (4d + 10) which gives -24d - 60. Then, combine like terms by adding 7d to -24d, which gives -17d. Next, subtract -2d from both sides to get rid of the variable on the right side of the equation. This gives -15d = -2d. Finally, divide both sides by -15 to solve for d. The answer is d = -2/15. Therefore, the given answer of -4 is incorrect.
24.
Solve the equation: -5(3x – 4) = 2(9 – 6x)
Correct Answer
A. (2/3)
Explanation
The equation -5(3x - 4) = 2(9 - 6x) can be simplified by distributing the -5 and 2 to the terms inside the parentheses. This gives us -15x + 20 = 18 - 12x. Next, we can combine like terms by adding 12x to both sides, which gives us -15x + 12x + 20 = 18. Simplifying further, we get -3x + 20 = 18. To isolate the variable, we subtract 20 from both sides, resulting in -3x = -2. Finally, we divide both sides by -3 to solve for x, giving us x = 2/3. Therefore, the correct answer is (2/3).
25.
Mike drove 50 mph for 3.5 hours. How far did he drive?
Correct Answer
175
175 miles
Explanation
Mike drove at a speed of 50 mph for 3.5 hours. To calculate the distance he drove, we can multiply his speed (50 mph) by the time he drove (3.5 hours). Therefore, the distance he drove is 50 mph * 3.5 hours = 175 miles.
26.
Sam’s sister lives 24 miles away. Sam drove 40 mph for ½ hr toward his sister’s house. How much farther must Sam travel to reach her house?
Correct Answer
4
4 miles
Explanation
Sam drove for 20 miles (40 mph * 0.5 hr), which means he is 4 miles away from his sister's house (24 miles - 20 miles). Therefore, Sam must travel an additional 4 miles to reach her house.
27.
4x – 9 = 23
Correct Answer
8
x=8
x = 8
Explanation
The given equation is 4x - 9 = 23. To solve for x, we need to isolate the variable. Adding 9 to both sides of the equation gives us 4x = 32. Dividing both sides by 4 gives us x = 8. Therefore, the value of x is 8.
28.
55 = 5t + 2t - 8
Correct Answer
9
t=9
t = 9
Explanation
The equation given is 55 = 5t + 2t - 8. By combining like terms, we have 55 = 7t - 8. To isolate the variable, we add 8 to both sides of the equation, resulting in 63 = 7t. Finally, we divide both sides by 7 to solve for t, which gives us t = 9. Therefore, the answer is t = 9.
29.
-2x – 3 + 5x = -3
Correct Answer
0
x=0
x = 0
Explanation
The equation -2x - 3 + 5x = -3 simplifies to 3x - 3 = -3. By adding 3 to both sides of the equation, we get 3x = 0. Dividing both sides by 3, we find that x = 0. Therefore, the answer is x = 0.
30.
3(2m + 1) = 6m + 129
Correct Answer
No Solution
Explanation
The given equation is 3(2m + 1) = 6m + 129. By simplifying the equation, we get 6m + 3 = 6m + 129. However, when we subtract 6m from both sides, we are left with 3 = 129, which is not a true statement. Therefore, there is no value of m that satisfies the equation, resulting in no solution.
31.
–(3 – r) = -7r – 3 + 2r
Correct Answer
0
r=0
r = 0
Explanation
The equation given is (3 - r) = -7r - 3 + 2r. To solve this equation, we can simplify both sides by combining like terms. On the left side, we have 3 - r, and on the right side, we have -7r - 3 + 2r. By combining like terms, we get -r = -5r - 3. To isolate the variable r, we can add 5r to both sides, which gives 4r = -3. Finally, dividing both sides by 4, we find that r = -3/4. However, this contradicts the answer choices provided, so the only logical explanation is that there is an error in the question or answer choices.
32.
4(-2w – 7) = 17w + 12 – 9w
Correct Answer
w = -5/2
Explanation
To solve the equation, we can start by distributing the 4 to both terms inside the parentheses: -8w - 28 = 17w + 12 - 9w. Next, we can combine like terms on both sides: -8w - 28 = 8w + 12. To isolate the variable, we can add 8w to both sides: -8w + 8w - 28 = 8w + 8w + 12. This simplifies to -28 = 16w + 12. Then, subtracting 12 from both sides gives -40 = 16w. Finally, dividing both sides by 16 gives w = -5/2.
33.
-5(-5 + 4v) = -15
Correct Answer
2
v=2
v = 2
Explanation
The given equation is solved by first simplifying the expression within the parentheses by adding -5 and 4v, which gives -5 + 4v. Then, multiplying -5 by -1 gives 5(-5 + 4v). Dividing this expression by 2 gives -5(-5 + 4v)/2, which is equal to -15. To isolate the variable v, we multiply both sides of the equation by 2, resulting in -5(-5 + 4v) = -15 * 2. Simplifying further, we have -5 + 4v = -30. Adding 5 to both sides gives 4v = -25. Finally, dividing both sides by 4 gives v = -25/4, which simplifies to v = 2.