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Verified Answer :

I got x= -4 i checked my work to and still got the same answer, i feel confident about my answer.

As your answer is given, it's impossible to solve because the result of the absolute value is always positive(or zero). 
But if |5x+13|=7

The are 2 cases:

1. 5x+13=-7
5x=-20
x=-4

2. -(5x+13)=-7
5x+13=7
5x=-6
x=-6/5

I hope that this is the answer that you were looking for and it has helped you.

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