Question

When solving for unknowns how does the values sometimes change and sometimes stay the same? (+&-)

Question: 2x+6 = x+16

Answer: 2x-x = 16-6
X=10

NOTE: This is an example from my text book with the answer in the text book right below it.

Answer 1

Not sure I understand your question fully, what do you mean by "sometimes change and sometimes stay the same" ?

Answer 2

I should of clarified more with the other example: This example one of the values changed and the other didn't

Example: 8x-12 = -3+21
Answer: 8x+3x = 21+12
11x= 33
x=3

Answer 3

oh you mean how the 8x stayed the same on the left side but the -12 turned into 3x?

Answer 4

in the first example were adding then in the answer were subtracting both then in the 2nd example were subtracting and adding then in the answer were adding both...maybe values was the wrong word to use.

Answer 5

You want to isolate x. So you want to get all the x terms to one side and everything else to the other side.


8x-12 = -3x+21


8x-12+3x = -3x+21 + 3x


8x+3x-12 = -3x+3x + 21


8x+3x-12 = 0x + 21


8x+3x-12 = 21


8x+3x-12+12 = 21+12


8x+3x = 21+12

Answer 6

so that's how they jumped from

8x-12 = -3x+21

to

8x+3x = 21+12

Answer 7

where do all the threes come from?

Answer 8

8x-12 = -3x+21

8x-12+3x = -3x+21 + 3x ... add 3x to both sides

I'm adding 3x to both sides because -3x+3x on the right side becomes 0x (and it goes away)

Answer 9

I do the same for 12 as well to move it over to the right side

Answer 10

would you always apply this for more then one unknown and would you always use the numbers from the right side?

Answer 11

you can apply this to any kind of linear equation

Answer 12

is it always the right side of numbers?

Answer 13

what do you mean

Answer 14

thats not what i meant, I meant how do you know what numbers to use?

Answer 15

oh you want to undo -3x

so you have to add 3x to make it 0x or just 0

Answer 16

that's why I added 3x to both sides

Answer 17

so if the number is a minus you want to turn it into a positive?

Answer 18

which the 12 and three are

Answer 19

yes, the opposite of - is +

Answer 20

ok i think i got it, about the first example i gave you where there both positive and in the answer there both negative?

Answer 21

2x+6 = x+16

2x+6-x = x+16-x ... Subtract x from both sides.

2x-x+6 = x-x+16

2x-x+6 = 0x+16

2x-x+6 = 16

2x-x+6-6 = 16-6 ... Subtract 6 from both sides.

2x-x = 16-6

Answer 22

so that's how they jumped from

2x+6 = x+16

to

2x-x = 16-6

Answer 23

@jim_thompson5910 you answer is great. I just want to add something that i think its easier to visualize.
Imagine a balance with dishes. Its the same thing, an equation is saying that somthing is equal to something else. To mantain the dishes balanced, if you take something of one side, then you need to take the same thing on the other to mantain the balance. Using this last example you used, you want to take the x of one side, so you need to tae it from the other as well, you want to take the six from the left, so you need to take six from the right to, everything o keep the balance, if you divide on one side, you divide it on the other as well, and the same thing with multiplication.