I can't figure out these math questions?!?

Question

if you have 2(3x+6)+8=6x, would that be a no answer type of question (like, if you have to solve the equation)? Also, How would you figure out 3(x+2)+1=2x+7+x because when I simplified everything, I ended up with 3x+7=3x+7... Please help!!

Answer 1

first be sure you're read it, and posted it right.

if you have, then it's not solvable.

you have 6x on one side and 6x on the other side, and they do cancel each other out.

when that happens, there is not a unique solution.

you could substitute 1 or 2 or 4 or anything for x, and the equation would be correct.

the 2nd is the same.

understanding that they are not solvable is just as accurate as solving them.

Answer 2

x  can be any number.

Answer 3

Wow i am so glad that i'm not in school anymore!

Answer 4

PROBLEM 1:

2(3x + 6) + 8 = 6x

6x + 12 + 8 = 6x

6x + 20 = 6x

Here you have gotten to an inconsistency.  In other words, if you subtract 6x from both sides you have:

20 = 0

Anytime you get to this case it means there is NO solution for x that will satisfy the equation.

Answer:

NO solutions

PROBLEM 2:

3(x+2) + 1 = 2x + 7 + x

3x +6 + 1 = 3x + 7

3x + 7 = 3x + 7

And when you get to a case like this, it means that ANY value of x will satisfy the equation.

Answer:

INFINITELY MANY solutions