Question

what is the solution to the inequality |2n+5|>1?
-3>n>-2
2-2 n<2 or n>3

Answer 1

\[|x|>c\] is the equivalent of saying
x>c and -x>c

Answer 2

|x|=x
|-x|=x

means, whether it is f(x) or -f(x), |f(x)|=|-f(x)|

so you have a function in n, f(n)=2n+5
you want to know when it is greater than 1, so if we let f(n)=1
we get

2n+5=1

also, we know that we can let -f(n)=1, since |f(n)|=|-f(n)|=1
so -(2n+5)=1

solve both for n

2n+5=1, n=-4/2=-2

-(2n+5)=1
-2n-5=1
-6=2n
-6/2=n
n=-3

so we know that n=-2, or n=-3
now we want to know what values of n, |2n+5|>1

we know that when n=-2, |2n+5|=1, and when n=-3, |2n+5|=1, now we would usually use a graph to show you this


from the shaded region, we can easily see that when n is between -2 and -3, that is, -3=<n<=-2, we have |f(n)|<=1, so we want |f(n)|>1, so we want where the function is above y=1
therefore, your answer will be n>-2, or n<-3