Question

Solve -4 < 3x+ 2 < =5.

Answer 1

Given:

There are given that the inequality:

$-4<3x+2\leq5$

Explanation:

To solve the above inequality, we need to use the inequality rule:

Then,

From the inequality rule:

$\begin{gathered} ifaSo,

Apply the above rule to the given inequality:

So,

From the inequality:

[tex]\begin{gathered} -4\lt3x+2\leqslant5 \\ -4<3x+2,and,3x+2\leq5 \end{gathered}$

Then,

$\begin{gathered} -4\lt3x+2, and, 3x+2\leqslant5 \\ -4-2<3x+2-2,and,3x+2-2\leq5-2 \\ -6<3x,and,3x\leq3 \end{gathered}$

Then,

$\begin{gathered} -6\lt3x, and, 3x\leqslant3 \\ -\frac{6}{3}\lt\frac{3x}{3},and,\frac{3x}{3}\leqslant\frac{3}{3} \\ -2Final answer:

Hence, the solution to the given inequality is shown below:

[tex]-2\lt x\leqslant1$