Give+an+example+of+an+equation+that+has+no+solution+Set+3

I 3x+4 I = -5 I agree. Why does this not have a solution?

This problem has no solution because an absolute value of some number cannot yield a negative number. The absolute value of a negative will always return a positive, because the absolute value refers to a number's distance from zero on a number line.

What about something like ⎮x² + 1 ⎮ = 0?  Although the absolute value of a number can return a zero, the only way to return a zero is if it is the absolute value of zero. In this case, no matter what you plug in for x, you will always receive a positive number due to the fact that x is being squared. If x is 0, the number in the absolute value bars is still going to be 1, which does not equal zero. In other words, it is impossible to make x^2 = -1, which would be necessary for making the x^2 +1 equal to zero.

l-3x+34l = 0

this last one certainly does have a solution; -3x + 34 must be equal to zero; -3x + 34 = 0, so -3x = -34, so x = 34/3!!