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Joelty · Answer 1 · 2023-03-27T04:12:14+0000

Given:

There are given that the inequality:

$-4<3x+2\leq5$

Step-by-step 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,

$\begin{gathered} -6\lt3x, and, 3x\leqslant3 \\ -(6)/(3)\lt(3x)/(3),and,(3x)/(3)\leqslant(3)/(3) \\ -2Final answer:Hence, the solution to the given inequality is shown below:[tex]-2\lt x\leqslant1$

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