What is the solution of |2x+3|=3x+5?

x = - 8 / 5

Step-by-step explanation:

There are 2 equations, since |x|=x when x>0 and |x|=-x when x<0

So, the first equation is

1. 2x+3=3x+5 when (x>0)

2. - 2x-3=3x+5 when (x<0)

Lets solve the first equation by moving terms, on one side x terms, and on the other, free terms. Thus we have the following result

x=-2, which is a contradiction since we stated earlier that x>0, so this leads us to claim that eq. 1 has no solutions

Now lest do something similar with eq. 2. We get the following result. x=-8/5

This results satisfies the condition stated earlier, that x<0

So, the system |2x+3|=3x+5 has only one solution, x = - 8/5