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.)