Help with algebra problems? -30n=-27n-63?

Question

its review from the other year that i dont remember

PLEASE HELP!

-30n=-27n-63

9y-1=y-25

14p-8 = 22 +20p

z+81 = 9z - 7

39 - 12w = 7 - 16w

-15v-40=23-8v

63-x=2x+3

32n+46=1+8n

12r-18=13r+18

-x-1=x-21

thanks so much

Answer 1

-30n=-27n-63

(+27n on both sides)

-3n= -63

(divide by -3 on both sides)

n=21

9y-1=y-25

(-y on both sides)

8y-1=-25

(+1 on both sides)

8y= -24

(divided by 8 on both sides)

y= -3

14p-8 = 22 +20p

(-14p on both sides)

-8 = 22+ 6p

(-22 on both sides)

-30= 6p

(divided by 6 on both sides)

-5=p

z+81 = 9z - 7

(-z on both sides)

81 = 8z -7

(+7 on both sides)

88=8z

(divided by 8 on both sides)

11=z

39 - 12w = 7 - 16w

(+16 w on both sides)

39+4w =7

(-39 on both sides)

4w= -32

(divided by 4 on both sides)

w= -8

I hope this helped but I'm not gonna do it all for you cause you wouldn't be able to check if you understand. Have fun with the rest! :) (seriously, have fun. It makes it easier, lol)

Answer 2

For single-variable linear algebraic equations like these, the solution method is to perform identical arithmetic operations to both sides of the equation at the same time in order to simplify the equation down until you are left with the answer: A single variable on one side of the equals sign, and a constant numeric value on the other side. Since you are doing the same thing to both sides, the equation will still be true; both sides will still equal each other.

Let's take this one for example:

63-x=2x+3

Step One: Add or subtract the same "amount" of x to both sides of the equation. In this case, you would add 1x to both sides, giving

63 = 3x + 3

Step Two: Now do the same thing with the constants: Here we would subtract 3 from both sides, giving

60 = 3x  (or 3x = 60, since we generally expect to see the variable on the left in the solution.)

Step Three: Now we strip the coefficient from the independent variable by dividing both sides by 3:

x = 20

_______________

One more:

-30n = -27n - 63

30n = 27n + 63   (If you prefer, you can first multiply both sides by (-1) for simplicity)

3n = 63   (after subtracting 27n from both sides)

n = 21   (after dividing both sides by 3)

or you could have done the last one without the initial sign inversion by saving that for last by dividing by a negative number:

-30n = -27n - 63

-3n = -63   (after ADDing 27n to both sides)

n = 21   (after dividing both sides by -3)

or, some people would prefer a "hybrid" approach:

-30n = -27n - 63

0 = 3n - 63   (after adding 30n to both sides)

3n = 63   (after adding 63 to sides and then flipping the two sides to put the variable on the left)

n = 21   (after dividing both sides by 3)

_____________________

HTH!

Answer 3

the first one is n=21

Answer 4

add 30n to both sides  30n-30n=30n-27n-63

0=3n-63  add 63 to both sides

63=3n+63-63

63=3n  divide by 3

63/3=3n/3  21=3