Consider the following equation: 4 + 6x = 6x + 4. Explain why the equation has many solutions.

Question

michele_laino · Answer

here, please subtract 4 from both sides, first

anonymous · Answer

I don't think they want you to solve it. They want you to explain why the solution has many solutions.

misty1212 · Answer

HI again!!

anonymous · Answer

Hi love!

misty1212 · Answer

the commutative law says $a+b=b+a$ always

michele_laino · Answer

ok! Another methos is the following:
please note that the left side is equal to the right side, so your equatiuon is an identity, and an identity is checked for infinite values of x

misty1212 · Answer

therefore 
$$4+6x=6x+4$$ always

misty1212 · Answer

it is the commutative law, but with variables, like $2+5=5+2$ it is $4+6x=6x+4$ same thing

anonymous · Answer

Awesome! How about this one: 2 + 2x = 3 + 2x. explain why the equation does NOT have a solution

misty1212 · Answer

x is a variable, but whatever it is on the left, it is the same number on the right
you got a number, you add 2 to it, it has to be different then if you add 3 to it

michele_laino · Answer

please subtract from both sides 2x

anonymous · Answer

Thanks!!!!!!

michele_laino · Answer

thanks!

misty1212 · Answer

like if i have ten dollars and you have ten dollar, i get 2 more, you get 3 more, we cannot have the same amount of money!

anonymous · Answer

Yup

anonymous · Answer

I'll post another question soon

misty1212 · Answer

$$\color\magenta\heartsuit$$