We are given the compound inequality:

\[
-8 \leq 5x - 3 < 7
\]

Let's solve it step by step.

### Step 1: Add 3 to all parts of the inequality
To eliminate the constant \(-3\) on the middle term, we add 3 to each part of the inequality.

\[
-8 + 3 \leq 5x - 3 + 3 < 7 + 3
\]

This simplifies to:

\[
-5 \leq 5x < 10
\]

### Step 2: Divide by 5
To isolate \(x\), we now divide all parts of the inequality by 5.

\[
\frac{-5}{5} \leq \frac{5x}{5} < \frac{10}{5}
\]

This simplifies to:

\[
-1 \leq x < 2
\]

### Final Answer:
The solution is:

\[
x \in [-1, 2)
\]

This means \(x\) is greater than or equal to \(-1\) and strictly less than 2.

Would you like further details on any of the steps? Here are some related questions to deepen your understanding:

1. How do you solve inequalities with variables on both sides?
2. What happens when you divide inequalities by a negative number?
3. Can you graph the solution to this inequality on a number line?
4. How do you solve compound inequalities with absolute values?
5. What is the difference between strict and non-strict inequalities?

**Tip:** When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the compound inequality -8 ≤ 5x - 3 < 7 step by step. This problem covers key algebraic concepts like solving linear inequalities using addition and division properties. Suitable for students in Grades 8-10.

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