8th Grade Math- Solving Equations with Variables on Both Sides?

Question

Im in 8th grade math- we are learning pre-algebra-- solving equations wit variables on bith sides i have NO idea how to do it here are some of the problems:
2n+12=5n
4(x-5)+2=x+3
4(y-2/4)=9(y+1/3)

If you can please help me.... or any good websites will help too. THANKS!! =]]

Answer 1

Your ultimate goal of solving algebraic equations is to isolate variables on one side (which are the letters, symbols, greek letters, etc.), and the numbers on the other side.

For instance:
2n+12=5n
You want to get the 'n's on one side, so you would substract 2n from each side

2n + 12 = 5
-2n -2n
12 = 3n

Then you want to find what the variable is, since the variable is connected to a number (this is called the coefficient) by multiplication, you would isolate this number, by the opposite of multiplying, which is dividing.

Remember to divide BOTH sides.

12 = 3n
---- ----
3 3

4 = n

And your answer is n=4.
____________________

Some problems will involve additional steps to inorder to isolate the variable.
4(x-5)+2=x+3

Using the distributive propery, distribute 4 to each term in the parentheses (x and -5). So it should look like this:
4x - 4(5) + 2 = x + 3

Multiply 4(5)

4x - 20 + 2 = x + 3

Combine -20 + 2

4x - 18 = x + 3

**You have just simplified the left side (multiply and add what ever you are able to.)

Isolate the variable by subtracting an x on both sides.

4x - 18 = x + 3
-x -x
3x - 18 = 3

Isolate the number by adding 18 to both sides.

3x - 18 = 3
+18 +18
3x = 21

Divide

3x =21
--- ----
3 3

x = 7

Do the same for this one:
4(y-2/4)=9(y+1/3)

Distribute 4y - 4(2/4) = 9(y) + 9(1/3)
Simplify 4y - 2 = 9y + 3
Isolate Variables:
4y - 2 = 9y + 3
-4y -4y
-2 = 5y + 3
Isolate Numbers:
-2 = 5y +3
-3 -3
-5 = 5y
Divide:
-5 = 5y
--- ---
5 5
-1 =y

Good luck, try http://www.regentsprep.org/ and click on Math A if you need more help!

http://www.mathematicshelpcentral.com/ may also help you!

Answer 2

first to do this you must collect like terms
b, 2n+12=5n
12=5n-2n (substract both sides by 2n)
12=3n
12/3=3n/3
4=n
a, 4(x-5)+2=x+3
(4x-20)+2=x+3
4x-18=x+3
4x-x=3+18
3x=21
x=7 divide both sides by 3
c, 4(y -2/4)=9(y+1/3)
4y-2=9y+3
4y-9y=3+2
-5y=5
y=-1 divide both sides by -5

Answer 3

well first of all u want to get it down to only one variable so take the first one for expamle

(2n-2n)+12 = 5n- 2n
12=3n and then u divide by the number that is in front of the variable so... 12/3=3/3n so... 4= n

if u need any more help email me or concact me on messenger

Answer 4

it takes too long to do the other 2 but i hav the first one
2n+12=5n
-2 -2
n+12=3n

3/12=4
n=4

feel free to IM me if u have any questions

Answer 5

You can't add 5 to the 7a, because the 5 is JUST a 5. Since 2a is on the other side of the equation, and it doesn't have to add or minus any extra numbers, you have to get rid of the 7a. So, 7a + 5 = 2a -7a -7a 5 = -5a Divide both sides by -5, a = -1

Answer 6

1.adding -2n
12=3n
dividing by 3
n=4

2.4(x-5)+2=x+3
adding -2
4(x-5)=x+1
4x-20=x+1
adding 20-x
3x=21
dividing by 3
x=7

3.4(y-1/2)=9y+3
4y-2=9y+3
adding 2-4y
0=5+5y
adding -5
5y=-5
dividing by 5
y=-1

Answer 7

2n+12=5n
12=3n
n=4

4x-20+2=x+3
4x-18=x+3
3x-18=3
3x=21
x=7

4y-2=9y+3
4y=9y+5
-5y=5
y= -1