what is the solution set of the inequality -20<4x-8<12?

To solve the inequality \(-20 < 4x - 8 < 12\), we can break it into two separate inequalities and solve them step by step.

### Step 1: Solve the left inequality \(-20 < 4x - 8\)

Add 8 to both sides:
\[
-20 + 8 < 4x
\]
\[
-12 < 4x
\]

Divide both sides by 4:
\[
-3 < x
\]
This can be rewritten as:
\[
x > -3
\]

### Step 2: Solve the right inequality \(4x - 8 < 12\)

Add 8 to both sides:
\[
4x < 12 + 8
\]
\[
4x < 20
\]

Divide both sides by 4:
\[
x < 5
\]

### Step 3: Combine the results

The solution to the compound inequality \(-20 < 4x - 8 < 12\) is the intersection of the two inequalities \(x > -3\) and \(x < 5\).

Therefore, the solution set is:
\[
-3 < x < 5
\]
In interval notation, this is written as:
\[
(-3, 5)
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve a compound inequality involving "or" rather than "and"?
2. What is the difference between strict inequalities (e.g., \(<\)) and non-strict inequalities (e.g., \(\leq\))?
3. How would the solution change if the inequality was \(-20 \leq 4x - 8 \leq 12\)?
4. How can you graph the solution set \(-3 < x < 5\) on a number line?
5. What does it mean when a solution set is expressed in interval notation?

**Tip:** When solving compound inequalities, always pay close attention to the direction of the inequality symbols and whether they include the boundary points (i.e., use \(<\) vs. \(\leq\)).

Learn how to solve the compound inequality -20 < 4x - 8 < 12 with a detailed step-by-step solution. This problem covers key mathematical concepts such as inequalities and compound inequalities. Suitable for high school students in Grades 9-12.

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