Answer
$n=-4\ or\ n=4$
Work Step by Step
We know that when we evaluate an absolute value, the result will be positive, regardless of the sign of what is inside of the absolute value bars. Thus, we consider that the variable could be either a positive or a negative number.
$|n|+3=7\longrightarrow$ subtract 3 from each side
$|n|+3-3=7-3\longrightarrow$ subtract
$|n|=4\longrightarrow$ definition of absolute value
$n=-4\ or\ n=4$
Check each solution.
$|-4|+3=4+3=7\checkmark$
$|4|+3=4+3=7\checkmark$
