\left|2x+1\right|>7
Question
\left|2x+1\right|>7
Solve the inequality
\text{Solve for }x
x \in \left(-\infty,-4\right)\cup \left(3,+\infty\right)
Evaluate
\left|2x+1\right|>7
\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
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Evaluate
2x+1>7
Move the constant to the right side
2x>7-1
Subtract the terms
2x>6
Divide both sides
\frac{2x}{2}>\frac{6}{2}
Simplify
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Evaluate
\frac{6}{2}
Rewrite the expression
\frac{3\times 2}{2}
Reduce the fraction
3
\frac{2x}{2}>3
Simplify
x>3
\begin{align}&x>3\\&2x+1<-7\end{align}
\text{Solve the inequality for }x
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Evaluate
2x+1<-7
Move the constant to the right side
2x<-7-1
Subtract the terms
2x<-8
Divide both sides
\frac{2x}{2}<\frac{-8}{2}
Simplify
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Evaluate
\frac{-8}{2}
Rewrite the expression
\frac{-4\times 2}{2}
Reduce the fraction
-4
\frac{2x}{2}<-4
Simplify
x<-4
\begin{align}&x>3\\&x<-4\end{align}
Solution
x \in \left(-\infty,-4\right)\cup \left(3,+\infty\right)