Solving equations with the variables on each side?

Question

ex:
17+2n=21+2n


i'm so cofused!!!!! please help? please explain everything.
i know it's like this because my teacher went over it.
17+2n=21+2n
-2n -2n

17=21....... but how do you know which one to use?? lke in this case you used -2n to subtract each side and whatever. but why couldn't u use the 21 or 17???? ughhh plz help!!!

also with this one
5+2(k+4)=5(k-3)

which one do u use to like subtract or add by??? plz help me?

Answer 1

for the first one you need to subtract 2n from both sides and also subtract 17 from both sides to get the n by itself

0 = 4
Once you subtract 2n from both side they cancel each other out so you end up with 0 = 4

There is no solution set for this problem

What your teacher did was to move the 2n over first to try to get the n variable alone you could have subtracted either the 21 or 17 first, but you would still end up with the same thing once you moved the 2n

For the second one, go ahead and multiply through the () to make it easier
5 + 2k+8 = 5k -15
Now combine the like terms on both sides of the equations

13 + 2k = 5k - 15

Now subtract 2k from both sides so you will end up with a positive k value

13 = 3k -15

Now that you have done that add 15 to both sides to get the 3k alone

28 = 3k

To get the k alone divide both sides by 3

28/3 = k

K is 28/3 or 9 and 1/3

Hope this helps you out

Answer 2

don't worry its simple
17+2n=21+2n
first subtract the 17 from the 21
rewrite it
2n=4+2n
now subtract the 2n from the 2n on the other side of the equation
0=4
so the answer is no solution

for the 5+2(k+4)= 5(k-3)
first use the distributive property
rewrite
5+2k+8=5k-15
no combine the like-terms
rewrite
13+2k=5k-15
now subtract the 2k from the 5k thats on the other side of the equation
13=3k-15
now add the 15 from the 13 thats on the other side of the equation
27=3k
now divide the 3k into the 27 like this
27
__ = k
3

so the answer is k=9

Answer 3

Hi,
Remember that the goal is to get the variables on one side, either side, and the numbers on the other side. Do that by using the properties of equalities.
The first expression doesn't have a solution. When you end up with an expression that is false, 17 does not equal 21, then the equation has no solution. In math terms that is called an inconsistent equation.
Now, for the second one:
5+2(k+4) = 5(k-3)
5 +2k +8 = 5k -15 (Use the distributive property for both terms inside the parentheses. That is, multiply both elements inside the preantheses by the element outside the parentheses.) (Ignore the dots. They're only to maintain proper spacing.
5 +2k +8 = 5k -15
....-2k ........ -2k
--------------------------
5 +8.........=3k -15

13=3k-15
+15.....+15
--------------------
28=3k
k = 28/3 (Divide each side by 3).

FE

Answer 4

umm your example doesn't make sense. You'll end up with 17 = 21.

To solve equation with variable on both sides, just transpose the term with the variable (move it to the left side but change the sign from (+) to (-) or vise versa).

Then perform the operation or simplify.

You can also subtract both sides of the equation by the term on the right with the variable, you get the same result.

your second example:
5+2(k+4)=5(k-3)

subtract both sides by 5(k-3)
5 + 2(k+4) - 5(k-3) = 5(k-3) - 5(k-3)
5 + 2(k+4) - 5(k-3) = 0

multiply this out:
5 + 2k + 8 -5k + 15 = 0
28 - 3k = 0
3k = 28
k = 28/3

Answer 5

Add (-2) to each side of the equation.
17+2n+-2n=21+2n+-2n
combine like terms
2n+-2n=0
17+0=21+2N+-2N=0
17=21+0
Solve,
17=21; It is an invalid equation the right and left sides do not match.
5+2(k+4)=5(k-3)
Distribute the 2 and eliminate the parenthesis.
5+2k+8=5k-15
Combine like terms on the left.
5+8=13
13+2k=5k-15
Add( -)5k to each side.
13+2k+(-)5=(-)15
Add a (-)13 to each side.
2k+(-)5k=(-)15+(-)13
Combine like terms.
2k+(-)5k=(-)3 & (-)15+(-)13=(-)28
Then,
(-)3k=(-)28
Divide,
k=(-)28/(-)3, divide two negatives and you get a positive answer.
or,
k=28/3=9.33333 or 9&1/3.
Hope this helps you.

Answer 6

Hi,
u have to first seperate the like retms and the unlike terms from the equaion...

so from Eq above,
-2n+2n=21-17
0n=4
n=0
==========================================
5+2(k+4)=5[k-3]
5+2k+8=5k-15
13+2k=5k-15
13+15=5k-2k
28=3k
k=28/3
k=9.33

Answer 7

You need to isolate the variable. 1. Combine like terms. 5y - 2y = 3y + 2 => 3y = 3y + 2 2. Subtract the variable from the side with the number(I forgot the real teerms for doing this). 3y = 3y + 2 -3y -3y => 0 = 2 So this problem has no real solutions. You need to isolate the variable. 1. Combine like terms. 5x + 2 = 2x - 10 => 5x + 2 = 2x - 10 2. Subtract the variable from the side with the lone number(I forgot the real teerms for doing this). If lone numbers are on both sides, subtract one variable from both sides and subtract one lone number from both sides. 5x + 2 = 2x - 10 -2x -2x => 3x + 2 = -10 -2 -2 => 3x = -12 Solve. 3x = -12 ---- ----- 3 3 x = -4

Answer 8

it doesnt matter which one you subtract or add... for example: 8k+3=3k-7 i would move the 3k to the left (by subtracting it) and the 3 to the right (by subtracting it) giving me 5k=-10 k=-2 but you could also go about it the opposite way and move the 8k to the right (by subtracting it) and add 7 to the left (by adding it)... this would give -5k=10 k=-2... make sense?

Answer 9

yeh... I think you set both sides to 0 so subtract 5k-15 from both sides and set to 0