Answer:
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
