Question

Solve each inequality.

$-2<3x+1<7$

Short answer

The value of the given inequality is $\left(-1,2\right).$

Step-by-step solution

Step 1- Given information

An inequality$-2<3x+1<7$.

Step 2- To solve the inequality

From the given information,

$\begin{array}{l}-2<3x+1<7\\ \Rightarrow -2-1<3x<7-1\\ \Rightarrow -3<3x<6\\ \Rightarrow \frac{-3}{3}<x<\frac{6}{3}\\ \Rightarrow -1<x<2\end{array}$

Step 3- Conclusion

Therefore, the $-2<3x+1<7=-1<x<2$.

Hence, the value of the given inequality is $\left(-1,2\right).$