Question

Please help, I'm currently confused on telling whether an absolute value equation has a solution or doesn't. For example, -5|x + 1| = 10 has no solution, and if you actually did it, the x would be -3, and 1. Meanwhile 2|x − 6| + 14 = 38 has a solution of x = −6, x = 18 and it has a solution??? I'm so confused.

Answer 1

Look at that first example

-5|x + 1| = 10
/-5. /-5
|x + 1| = -2
An absolute value can’t equal a negative and still be a real number … so there are no real solutions. It’s that negative!