-4=5n+6 home work

Question

mult step equaltions 

Answer 1

Problem: 5n + 6 = -4

 

The first step is to isolate the variable (n) on one side of the equation- in other words, you want to get n by itself on one side of the equals sign.

 

If 5n + 6 equals -4, the first step is to move the 6 to the other side of the equation, to the side with the negative 4, so you subtract 6 from 5n + 6 (because when you subtract 6 from 5n + 6 you are canceling out the six on that side of the equation). Now that you have subtracted 6 from 5n+6 you need to do the same thing on the other side of the equation. Why do you need to subtract 6 from -4? Because if 5n + 6 = -4, you are saying 5n + 6 is -4, so when you subtract 6 from 5n + 6, you now have 6 less than what you started with, so you have to subtract 6 from -4 as well.

 

-4 - 6 will give you -10. So your first step will look like this:

 

5n + 6 = -4

5n + 6 - 6 = -4 - 6

5n + 6 - 6 = -4 - 6

 

5n = -10

 

Then, divide both sides by 5 to figure out what n is.  You divide 

 

5n ÷ 5 = -10 ÷ 5

5n ÷ 5 = -10 ÷ 5 

 

The 5s cancel out on the left hand side because 5 ÷ 5 = 1, so you are left with 1 × n which equals n.

 

So then n = -10 / 5

And      n = -2

 

So because  n is -2, 5 negative 2s, will give you 5n. 

Answer 2

To solve this equation, our goal is to get the variable (n) on one side of the equation, and a number on the other side.

 

Our first step is to get any numbers not connected to the variable over to the other side of the equation. We need to subtract 6 from both sides of the equation.

 

-4 = 5n + 6

- 6      - 6

 

-4 - 6 is the same as -4 + -6, so we get:

 

-10 = 5n

 

Now we want to get the n alone, so we need to divide both sides by 5. We divide because we need to do the inverse operation of what is currently in the equation, which is multiplication. We know this because 5n means 5 x n or 5 multiplied by n.

 

-10 = 5n

 /5      /5

 

-2 = n

 

Our answer is -2 because when dividing a negative number by a positive number, the quotient is negative.

 

To check our work, we can substitute -2 in for n and make sure that our equation works:

 

-4 = 5 (-2) +6

-4 = -10 + 6

-4 = -4