Solve −7<3𝑥+2≤5−7<3x+2≤5.

Sure, let's solve this inequality step by step.

The inequality is -7 < 3x + 2 ≤ 5.

First, let's split this compound inequality into two separate inequalities:

-7 < 3x + 2 and 3x + 2 ≤ 5.

Now, let's solve each inequality separately.

For -7 < 3x + 2, we subtract 2 from both sides to isolate the term with x:

-7 - 2 < 3x, which simplifies to -9 < 3x.

Then, we divide both sides by 3 to solve for x:

-9/3 < x, which simplifies to -3 < x.

For 3x + 2 ≤ 5, we subtract 2 from both sides to isolate the term with x:

3x ≤ 5 - 2, which simplifies to 3x ≤ 3.

Then, we divide both sides by 3 to solve for x:

x ≤ 3/3, which simplifies to x ≤ 1.

So, the solution to the inequality -7 < 3x + 2 ≤ 5 is -3 < x ≤ 1.