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Mathematics
31 December, 05:10
What is the solution of |2x+3|=3x+5?
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Kyson
31 December, 05:19
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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
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