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To solve the compound inequality:

\[
-10 < 4x - 2 \leq 10
\]

we can break it down into two parts:

### Step 1: Solve the left inequality
\[
-10 < 4x - 2
\]

Add 2 to both sides:
\[
-10 + 2 < 4x
\]
\[
-8 < 4x
\]

Then, divide by 4:
\[
-2 < x
\]

This gives us:
\[
x > -2
\]

### Step 2: Solve the right inequality
\[
4x - 2 \leq 10
\]

Add 2 to both sides:
\[
4x \leq 12
\]

Then, divide by 4:
\[
x \leq 3
\]

### Combine the Results
The solution for the compound inequality is:
\[
-2 < x \leq 3
\]

### Graphing the Solution
On the number line:
- Draw an open circle at \( x = -2 \) (since \( x > -2 \) does not include -2).
- Draw a closed circle at \( x = 3 \) (since \( x \leq 3 \) includes 3).
- Shade the region between \( x = -2 \) and \( x = 3 \).

Would you like more details on each step, or have any questions about this solution?

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Here are 5 related questions to expand your understanding:
1. How would the solution change if the inequality were \( -10 \leq 4x - 2 < 10 \)?
2. How do you solve a compound inequality with "or" instead of "and"?
3. What are the steps to graph a strict inequality versus a non-strict inequality on a number line?
4. How can we verify that our solution to a compound inequality is correct?
5. How does dividing or multiplying by a negative number affect an inequality?

**Tip:** Always pay attention to the inequality signs, especially when dividing by negative numbers, as they reverse the direction of the inequality.

Solve the compound inequality: -10 < 4x - 2 ≤ 10 and graph the solution on the number line.

Learn how to solve and graph the compound inequality -10 < 4x - 2 ≤ 10. This problem covers important algebraic techniques, including isolating variables in inequalities and graphing solutions on a number line. Ideal for students in Grades 7-10.

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