Beagleboy how do I explain that in 50 words?

Post your 50-word 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.

In the first equation, -6(x + 3) = -6x + 5, when simplified, we get -6x - 18 = -6x + 5. By simplifying further, we see that -6x = -6x - 23, which implies that -23 = 0. However, this is not true, indicating no solution. In the second equation, after simplifying, 7x + 18 + 8x = 8(x + 4) + 7x - 14, we get 15x + 18 = 15x - 2. By simplifying further, we find 18 = -2, which is not true. This indicates infinitely many solutions.