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Chapter 2: Q66. (page 67)

Solve each inequality.
$- 2 < 3 x + 1 < 7$

Short Answer

Expert verified

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

Step by step solution

01

Step 1- Given information

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

02

Step 2- To solve the inequality

From the given information,

$\begin{array}{l} 鈭� 2 < 3 x + 1 < 7 \\ 鈬� 鈭� 2 鈭� 1 < 3 x < 7 鈭� 1 \\ 鈬� 鈭� 3 < 3 x < 6 \\ 鈬� \frac{鈭� 3}{3} < x < \frac{6}{3} \\ 鈬� 鈭� 1 < x < 2 \end{array}$

03

Step 3- Conclusion

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

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

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