Solve the equation below. Choose the method you prefer to use. Check your answer.
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n/6 - 5n/12 = 1/6
n= (Type an integer or a simplified fraction)
To solve the equation, we can start by finding a common denominator for the fractions on the left side of the equation, which is 12. This allows us to rewrite the equation as:
2n/12 - 5n/12 = 1/6
Combining the fractions on the left side, we have:
(2n - 5n)/12 = 1/6
Simplifying the numerator, we get:
(-3n)/12 = 1/6
Multiplying both sides of the equation by 6 to eliminate the fractions, we have:
6*(-3n)/12 = 6*(1/6)
Simplifying further, we get:
-3n/2 = 1
To solve for n, we can multiply both sides of the equation by 2 to eliminate the fraction:
2*(-3n/2) = 2*1
Simplifying, we have:
-3n = 2
Dividing both sides of the equation by -3, we get:
n = 2/(-3)
Simplifying the fraction, we have:
n = -2/3
Therefore, the solution to the equation is n = -2/3. We can check this by substituting this value back into the original equation:
-2/3/6 - 5(-2/3)/12 = 1/6
Simplifying, we get:
(-2/18) - (-10/36) = 1/6
-1/9 + 5/18 = 1/6
(2/18) + (5/18) = 1/6
7/18 = 1/6
The equation is true, so our solution n = -2/3 is correct.
Solve the equation.
8n - (5n + 7) = 5
n= enter your response here (Simplify your answer.)
To solve the equation 8n - (5n + 7) = 5, we can simplify the expression inside the parentheses first:
8n - 5n - 7 = 5
Combine like terms on the left side:
(8n - 5n) - 7 = 5
3n - 7 = 5
Now, let's isolate the variable by adding 7 to both sides:
(3n - 7) + 7 = 5 + 7
3n = 12
Finally, divide both sides by 3 to solve for n:
3n/3 = 12/3
n = 4
Therefore, the solution to the equation is n = 4.
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Part 1
Angie and Kenny play online video games. Angie buys 1 software package and 1 month of game play. Kenny buys 2 software packages and 5 months of game play. Each software package costs $50. If their total cost is $240, what is the cost of one month of game play?
Let's assume the cost of one month of gameplay is x dollars.
Angie buys 1 software package, which costs $50, and 1 month of gameplay (x dollars).
Kenny buys 2 software packages, which cost $50 each (2*50 = $100), and 5 months of gameplay (5x dollars).
The total cost for Angie and Kenny is $240, so we can set up the equation:
50 + x + 100 + 5x = 240
Combining like terms, we have:
6x + 150 = 240
Next, let's isolate the variable by subtracting 150 from both sides:
6x + 150 - 150 = 240 - 150
6x = 90
Finally, divide both sides by 6 to solve for x:
6x/6 = 90/6
x = 15
Therefore, the cost of one month of gameplay is $15.
Solve.
10x + 16 = 6x - 8
x=
To solve the equation 10x + 16 = 6x - 8, we can start by isolating the variable x.
First, let's move all terms containing x to one side of the equation by subtracting 6x from both sides:
10x - 6x + 16 = 6x - 6x - 8
Simplifying the equation, we have:
4x + 16 = -8
Next, let's isolate the variable x by subtracting 16 from both sides:
4x + 16 - 16 = -8 - 16
Simplifying further, we have:
4x = -24
Finally, divide both sides of the equation by 4 to solve for x:
4x/4 = -24/4
x = -6
Therefore, the solution to the equation is x = -6.
Solve the equation. Check your solution.
9y - 8 = 18 - 4y
y=
To solve the equation 9y - 8 = 18 - 4y, we can start by isolating the variable y.
First, let's move all terms containing y to one side of the equation by adding 4y to both sides:
9y - 8 + 4y = 18 - 4y + 4y
Simplifying the equation, we have:
13y - 8 = 18
Next, let's isolate the variable y by adding 8 to both sides:
13y - 8 + 8 = 18 + 8
Simplifying further, we have:
13y = 26
Finally, divide both sides of the equation by 13 to solve for y:
13y/13 = 26/13
y = 2
Therefore, the solution to the equation is y = 2.
To check our solution, let's substitute y = 2 back into the original equation:
9(2) - 8 = 18 - 4(2)
18 - 8 = 18 - 8
10 = 10
The equation is true, so our solution y = 2 is correct.
Solve the equation. Check your solution.
-4y + 7 = 35y - 6
y= enter your response here (Type an integer or a simplified fraction.)
To solve the equation -4y + 7 = 35y - 6, we can start by isolating the variable y.
First, let's move all terms containing y to one side of the equation by subtracting 35y from both sides:
-4y + 7 - 35y = 35y - 35y - 6
Simplifying the equation, we have:
-39y + 7 = -6
Next, let's isolate the variable y by subtracting 7 from both sides:
-39y + 7 - 7 = -6 - 7
Simplifying further, we have:
-39y = -13
Finally, divide both sides of the equation by -39 to solve for y:
(-39y)/-39 = (-13)/-39
y = 1/3
Therefore, the solution to the equation is y = 1/3.
To check our solution, let's substitute y = 1/3 back into the original equation:
-4(1/3) + 7 = 35(1/3) - 6
-4/3 + 7 = 35/3 - 6
-4/3 + 7 = 35/3 - 18/3
(21/3) - (18/3) = (35/3) - (18/3)
3/3 = 17/3
The equation is true, so our solution y = 1/3 is correct.
Solve the equation. Check your answer.
3(x - 5) = 2( x 5)
x = enter your response here(Type an integer or a simplified fraction.)
To solve the equation 3(x - 5) = 2(x + 5), let's distribute the multiplication on both sides:
3x - 15 = 2x + 10
Next, let's isolate the variable x by subtracting 2x from both sides:
3x - 2x - 15 = 2x - 2x + 10
Simplifying the equation, we have:
x - 15 = 10
Now, let's isolate the variable x by adding 15 to both sides:
x - 15 + 15 = 10 + 15
Simplifying further, we have:
x = 25
Therefore, the solution to the equation is x = 25.
To check our answer, let's substitute x = 25 back into the original equation:
3(25 - 5) = 2(25 + 5)
3(20) = 2(30)
60 = 60
The equation is true, so our solution x = 25 is correct.
Determine whether the equation is an identity or whether it has no solution.
2(a-6) = 4a - (2a + 12)
To determine whether the equation 2(a-6) = 4a - (2a + 12) is an identity or has no solution, let's simplify the equation:
Expanding the parentheses on the right side of the equation, we have:
2(a-6) = 4a - 2a - 12
Simplifying further, we have:
2a - 12 = 2a - 12
At this point, we can observe that both sides of the equation are equal. The equation is an identity, meaning it holds true for all values of a.
Therefore, the equation is an identity.
Determine whether the equation below is an identity or whether it has no solution.
-7(7x+4) = -49x+28
To determine whether the equation -7(7x+4) = -49x+28 is an identity or has no solution, let's simplify the equation:
Expanding the parentheses on the left side of the equation, we have:
-49x - 28 = -49x + 28
At this point, we can observe that the variable terms (-49x) on both sides of the equation cancel out.
-28 = 28
This equation is not true, as -28 is not equal to 28. Therefore, the equation has no solution.
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $73. A season ski pass costs $400. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Let's denote the number of days the skier goes skiing as "d".
The cost of using daily passes for "d" days would be:
Cost of daily passes = ($73 + $30) * d
The cost of purchasing a season ski pass and renting skis for "d" days would be:
Cost of season pass = $400 + ($30 * d)
We want to find the number of days, "d", for which the cost of the season pass is less than the cost of daily passes.
Setting up the equation:
($73 + $30) * d > $400 + ($30 * d)
Expanding and simplifying:
$103d > $400 + $30d
Subtracting $30d from both sides:
$103d - $30d > $400
Simplifying further:
$73d > $400
Dividing both sides by $73:
d > $400/$73
Calculating the value on the right:
d > 5.48
Since "d" represents the number of days, it cannot be a fraction. Therefore, the skier would need to go skiing for at least 6 days in order for the season pass to be less expensive than using daily passes.
Note: The skier would save money with the season pass if they plan on skiing for 6 or more days during the season.
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
Curtis is working on an essay. He copies and pastes a sentence into his essay. He makes sure to include quotation marks and properly cites his source.
(1 point)
Responses
Yes
Yes
No
No
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
Pam posts an answer to a test question on Facebook.
(1 point)
Responses
Yes
Yes
No
Yes
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
Sue finds the answers to her portfolio online. She changes the name on the portfolio and submits it as her own work.
(1 point)
Responses
Yes
Yes
No
Yes
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
Paul spends 60 seconds on his 10 question quiz. He gets all of the answers wrong.
(1 point)
Responses
Yes
Yes
No
No
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
LeShawn studies with his friend. They go over all of the key words for the lesson and look up answers to the practice questions in their textbooks. They both take the test independently of each other.
(1 point)
Responses
Yes
Yes
No
No
No
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
Liza’s Learning Coach sits beside her while she is taking a test and helps her with some of the more difficult questions.
(1 point)
Responses
Yes
Yes
No
Yes
Determine if the scenario is considered academic dishonesty. If a situation is academic dishonesty, select Yes. If it does not violate any rules, select No.
Cathy is taking her test. She does not know the answer to question 5, so she Googles the question, finds an answer, then copies and pastes the answer into the test.
(1 point)
Responses
Yes
Yes
No
No