ALGEBRA
posted by SAMANTHA on .
Beagleboy how do I explain that in 50 words?
Post your 50word response to the following:
Explain why the equation 6(x + 3) = 6x + 5 has no solution and 7x +18 + 8x = 8(x + 4) + 7x – 14 has infinitely many solutions.

Can anyone help me I need to explain this problem in 50 words.
Explain why the equation 6(x + 3) = 6x + 5 has no solution and 7x +18 + 8x = 8(x + 4) + 7x – 14 has infinitely many solutions. 
solving the first gives us
0 = 23 which is nonsense, thus no solution.
solving the second gives us
0 = 0 which is true, thus any value of x will work > an infinite number of solutions.
In general:
if the variable drops out, and
you end up with true statement > infinite number of solutions
if you end up with a false statement > no solution.