\text{Separate the inequality into }2\text{ possible cases}
\begin{align}&2x+1>7\\&2x+1<-7\end{align}
\text{Solve the inequality for }x
Move the constant to the right side
2x>7-1
Subtract the numbers
2x>6
Divide both sides
\frac{2x}{2}>\frac{6}{2}
Divide the numbers
x>\frac{6}{2}
\begin{align}&x>3\\&2x+1<-7\end{align}
\text{Solve the inequality for }x
Move the constant to the right side
2x<-7-1
Subtract the numbers
2x<-8
Divide both sides
\frac{2x}{2}<\frac{-8}{2}
Divide the numbers
x<\frac{-8}{2}
\begin{align}&x>3\\&x<-4\end{align}
x \in \left(-\infty,-4\right)\cup \left(3,+\infty\right)
