\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
Multiply both sides
2x\times \frac{1}{2}>6\times \frac{1}{2}
Reduce the numbers
2x\times \frac{1}{2}>3
\text{Cancel out the greatest common factor }2
x>3
\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
Multiply both sides
2x\times \frac{1}{2}<-8\times \frac{1}{2}
Reduce the numbers
2x\times \frac{1}{2}<-4
\text{Cancel out the greatest common factor }2
x<-4
\begin{align}&x>3\\&x<-4\end{align}
x \in \left(-\infty,-4\right)\cup \left(3,+\infty\right)
