math question for my 5th grader, 3n(14 + 1/n)=5n, whats the answer and can someone explain?

Answer 1

Here's another explanation.

First, multiply both the numbers inside the parentheses by the number outside of them on the left side.

3n x 14 = (3 x 14) x n = 42n
3n x (1/n) = (3 x 1) x ( n/n) = 3 (n/n)* = 3 (1)* = 3
*This is true because any number divided by itself is 1.

Now, add the two numbers together and equate them with the other side:

1) 42n + 3 = 5n
2) (42n - 5n) + (3 - 3) = (5n - 5n) - 3
3) 37n = -3
4) 37n / (37) = -3 / (37)
5) n = -3 / 37

In the second step above, we subtracted 5n and 3 from both sides of the equation to get the number containing the variable (n) on one side of the equation, and show the result in step 3. Then, in the fourth step, we divided both sides of the equation by 37 to find what n is. Remember, when dealing with equations, whatever you do to one side, you must also do to the other side. Otherwise, they do not remain equal.

To verify that n = -3 / 37, we can put it back in the equation everywhere n appears and see if the result is true. If it is, we are done.

1) 3n(14 + 1/n)=5n
2) 3 (-3 / 37)[(14 + (37 / -3)] = 5 (-3 / 37)
3) (-9 / 37)(14) + (-9 / 37)(37 / -3) = -15 / 37
4) (-126 / 37) + (-9 / -3) = -15 / 37
5) (-126 / 37) + 3 = -15 / 37
6) (-126 / 37) + 3 (37) / 37 = -15 / 37
7) (-126 / 37) + 111 / 37 = - 15 37
8) (-126 + 111) / 37 = -15 / 37
9) -15 / 37 = -15 / 37

In the above sequence of steps, we invert -3 / 37, on step 2 because a fraction divided into 1 yields its reciprocal. For example, 1 / (1/2) = 2/1 = 2 because there are two halves in one whole. In step 3, we multiply the numbers together, and put the results in step 4. In step 5 we get 3 when we divide -9 by -3 because a negative number divided by another negative number yields a positive number. In step 6 we convert 3 to 37ths so we can add fractions. In step 8 we add the numerators of the two fractions. In step 9 we see that the two sides of the equation are equal, so our solution is correct and we are done with this problem.

Answer 2

To solve that, we have to use pure algebra, and go step by step, slowly.
The first thing we could do here is divide both sides by 3n
Hence:
= (14+1/n)= 5/3
Then, we find a common denominator that we could use for all of the equation. The LCD (Least Common Denominator) is 3n in this case. Therefore we multiply the 14 by 3n(numerator and denominator.); the 1/n by 3 and the 5/3 by n (all of them, numerator and denominator)
Therefore
= 42n/3n + 3/3n = 5n/3n
Now we multiply both sides by 3n, eliminating the denominator
= 42n + 3 = 5n
And we solve for n
= 42n - 5n= -3
= 37n= - 3
n = -3/37

Answer 3

3n(14+1/n)=5n

Divide n to both sides

This leaves us with 3(14+1/n)=5

Then, when you use distribution, you come up with 42+3/n=5.

Subtract 42 from both sides

3/n = -37

n = -3/37

Answer 4

3n(14 + 1/n) = 5n
or 3n(14 + 1/n) - 5n = 0
or n{3(14 + 1/n) - 5} = 0
or n(42 + 3/n - 5) = 0
or n(37 + 3/n) = 0

As product of two quantities = 0 so either one = 0.
So either n = 0 or 37 + 3/n = 0 i.e. n = - 3/37

Answer 5

3n(14+1/n)=5n

Divide both sides by n

So now, we have 3(14+1/n)=5

So: 42+3/n=5, subtract 42 from both sides

3/n=-37
n=-3/37

Answer 6

3n (14 + 1/n) = 5n
Multiply the brackets out on the left:
3n (14) + 3n(1/n) = 5n
=> 42n + 3 = 5n
Bring the 5n over to the left and the 3 to the right:
42n - 5n = -3
=> 37n = -3
=> n = -3/37.

Answer 7

3n(14+ (1/n)) = 5n (divide by N)
3(14+(1/n)) = 5 (simplify)
3(14) + 3(1/n) = 5 (multiply)
42 + (3/n) =5 (Subtract 42)
3/n = (-37) (multiply by N)
3 = (-37)N (divide by -37)
-3/37= N

Answer 8

you can do anything to an equation provide you do the same thing to both side of the equal sign:

divide by n: 3(14+1/n)=5

perform indicated operations: 42 +3/n = 5

subtract 42: 3/n = -37

multiply by n: 3 = -37n

divide by -37: 3/-37 = n

Answer 9

-4 + 5 = 1 --7 = 8 + - 8 = 0

Answer 10

(14+1/n)=5n/3n -->14+1/n=5/3 -->1/n=5/3-14-->1/n=(5-14*3)/3
-->n=3/(5-14*3)