answer comparison please

Answer 1

Once they combine like terms they will have

8x+11=27

the "subtraction property of equality" is just subtracting the same thing on both sides (in this case 11)

8x+11-11=27-11

after combining those like terms (left sides adds to zero, right side to 16)

8x=16

The "division property of equality" is just dividing the same thing on both sides (in this case 8)

8x/8=16/8

Then we simplify one last time to get...

x=2

"An equation that contains fractions". Well let's think about it with a simple equation

y = 1/2x

x=0 gets us 0

x = 1 gets us 1/2

x=2 gets us 1

Furthermore I can say that 1/1 is a fraction and 2/1 is a fraction, but those are the same as 1 and 2

The answer is sometimes. Whenever you see something in math that is NEVER or ALWAYS, be very careful. Its easy to disprove them with one example, while proving them is a lot harder.

To check the solution of an equation...

Let's say we have the first equation

3x+7+5x+4=27

Once you have a final answer (x=2), you can substitute (plug in) the solution for its variable (in this case x)

Replacing it we get...

3(2) + 7 + 5(2) + 4 = 27

Then we do multiplication and addition for each side and see if the equation is true

6 + 7 + 10 + 4 = 27

13 + 14 = 27

27 = 27

Its true, because 27 is equal to 27. If we had 23=27 or any simplified number besides 27 that would be false.