https://r2.erweima.ai/mathbot/image/1725889915334z4sdvagu.jpg

Let's solve the compound inequality given in the image:

The inequality is:

\[
-6 < x + 1 < 3
\]

### Step 1: Isolate \(x\)
To isolate \(x\), we first subtract 1 from all parts of the inequality:

\[
-6 - 1 < x + 1 - 1 < 3 - 1
\]

Simplifying the result:

\[
-7 < x < 2
\]

### Step 2: Write the solution in interval notation
The solution is all values of \(x\) that satisfy \(-7 < x < 2\). In interval notation, this is:

\[
(-7, 2)
\]

Thus, the correct answer is **A**: The solution set in interval notation is \((-7, 2)\).

Would you like more details on graphing the solution or any further clarifications?

### Related Questions:
1. How would the solution change if the inequality was \( \leq \) or \( \geq \)?
2. How do you graph the solution of a compound inequality like this?
3. Can a compound inequality have no solution? If so, under what conditions?
4. What is the difference between strict inequalities and non-strict inequalities?
5. How would this solution change if the inequality had been multiplied or divided by a negative number?

#### Tip: 
When solving inequalities, always remember that multiplying or dividing by a negative number reverses the inequality sign!

Solve and graph the compound inequality: -6 < x + 1 < 3

Learn how to solve the compound inequality -6 < x + 1 < 3 by isolating the variable x and expressing the solution in interval notation. The step-by-step solution walks through algebraic manipulation and provides the final answer in the form (-7, 2). Suitable for students in Grades 7-9.

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