please help me solve my homework with all the work involved. i have trouble paying attention in class so it's hard for me to do my homework. here are a few of the questions. I need to find out what the letters equal.
1.) 10(-4+y)=2y
2.)9(b-4)-7b=5(3b-2)
3.)-(8n-2)=3+10(1-3n)
4.)1/4(60+16s)=15+4s
Thank you a lot.
I'll do two of them for you. Which two would you like me to do?
The first two please
10(-4+y)=2y
-40 + 10y = 2y
-40 = 2y - 10y
-40 = -8y
-40/-8 = y
5 = y
_______________________
9(b-4)-7b=5(3b-2)
9b - 36 - 7b = 15b - 10
2b - 15b = 36 - 10
-13b = 26
b = -2
Of course, I'd be happy to help you with your homework! I understand that it can be challenging when you have trouble paying attention in class. Let's go through each question step by step and solve them together:
1.) 10(-4+y) = 2y
To solve this equation, we need to distribute the 10 to each term inside the parentheses:
10 * -4 + 10 * y = 2y
Simplifying further:
-40 + 10y = 2y
Next, let's isolate the terms with y on one side of the equation. We can do this by subtracting 2y from both sides:
-40 + 10y - 2y = 2y - 2y
Simplifying further:
-40 + 8y = 0
Now, to isolate the term with y, we can add 40 to both sides:
-40 + 40 + 8y = 0 + 40
Simplifying further:
8y = 40
Finally, we can solve for y by dividing both sides by 8:
8y/8 = 40/8
Simplifying further:
y = 5
So, the value of y in this equation is 5.
2.) 9(b-4) - 7b = 5(3b-2)
Let's simplify both sides of the equation first:
9b - 36 - 7b = 15b - 10
Next, let's combine like terms on each side of the equation:
(9b - 7b) - 36 = (15b) - 10
Simplifying further:
2b - 36 = 15b - 10
Now, let's isolate the terms with b on one side of the equation. We can do this by subtracting 2b from both sides:
2b - 36 - 2b = 15b - 10 - 2b
Simplifying further:
-36 = 13b - 10
Next, let's isolate the constant terms on one side of the equation by adding 10 to both sides:
-36 + 10 = 13b - 10 + 10
Simplifying further:
-26 = 13b
Finally, we can solve for b by dividing both sides by 13:
-26/13 = 13b/13
Simplifying further:
b = -2
So, the value of b in this equation is -2.
3.) -(8n - 2) = 3 + 10(1 - 3n)
Let's simplify both sides of the equation first:
-8n + 2 = 3 + 10 - 30n
Next, let's isolate the terms with n on one side of the equation. We can do this by adding 8n to both sides:
-8n + 8n + 2 = 3 + 10 - 30n + 8n
Simplifying further:
2 = 3 + 10 - 22n
Now, let's isolate the constant terms on one side of the equation by subtracting 3 and 10:
2 - 3 - 10 = 3 + 10 - 22n - 3 - 10
Simplifying further:
-11 = -22n
Finally, we can solve for n by dividing both sides by -22:
-11/-22 = -22n/-22
Simplifying further:
n = 1/2
So, the value of n in this equation is 1/2.
4.) 1/4(60 + 16s) = 15 + 4s
Let's simplify both sides of the equation first:
(1/4) * 60 + (1/4) * 16s = 15 + 4s
Simplifying further:
15 + 4s = 15 + 4s
In this case, notice that both sides of the equation are the same. This means that the infinite solutions exist for this equation. Any value of s would make both sides of the equation equal.
Therefore, there is no unique solution for this equation. The value of s can be any real number.
I hope this helps you understand how to solve these equations step by step. If you have any further questions or need more assistance, feel free to ask!