https://file.aiquickdraw.com/mathbot/file/17292496726798unoe3ww.jpg

The inequality in the image is \(|9x + 7| < 48\), which is an absolute value inequality. To rewrite this as two linear inequalities, we need to follow these steps:

### Step 1: Remove the absolute value
The general rule for solving \(|A| < B\) is to rewrite it as two inequalities:
\[
-B < A < B
\]
In your case, \(A = 9x + 7\) and \(B = 48\), so:

\[
-48 < 9x + 7 < 48
\]

### Step 2: Solve the inequalities
Now, we solve this compound inequality:

1. First, subtract 7 from all parts of the inequality:
\[
-48 - 7 < 9x < 48 - 7
\]
\[
-55 < 9x < 41
\]

2. Next, divide the entire inequality by 9 to isolate \(x\):
\[
\frac{-55}{9} < x < \frac{41}{9}
\]
So the final solution is:
\[
-\frac{55}{9} < x < \frac{41}{9}
\]

### Answer for the inequality boxes:
- The first box will contain \(-\frac{55}{9} < x\)
- The second box will contain \(x < \frac{41}{9}\)
- The correct word to select is "and" because this is a compound inequality.

Would you like further details or clarifications on this? Here are some additional practice questions you can try:

1. Rewrite \(|3x - 2| \leq 10\) as a compound inequality.
2. Solve \(|7x + 5| > 20\) and express it as two inequalities.
3. What is the solution to \(|4x - 9| \leq 12\)?
4. How would you express \(|5x + 1| \geq 15\) as two inequalities?
5. Solve the inequality \(|6x - 7| < 13\).

**Tip:** For absolute value inequalities, always consider whether you're dealing with a "less than" or "greater than" scenario, which will determine whether you use "and" or "or" in the final solution!

Consider the following absolute value inequality: |9x + 7| < 48. Rewrite the given inequality as two linear inequalities.

Learn how to solve the absolute value inequality |9x + 7| < 48 by rewriting it as two linear inequalities: -48 < 9x + 7 < 48. This step-by-step guide breaks down the algebraic process for solving absolute value inequalities, suitable for students in Grades 8-10.

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