It looks like you've uploaded an image. Let me extract and analyze the mathematical content from it to help with your query. I'll be right back with my findings! PIL import Image

Load and display the image to examine its content

image_path = '/mnt/data/1733664929813pljb78rg.jpg' image = Image.open(image_path) image.show()It seems I need to analyze the contents of the image to extract the math from it. Let me process it and extract the information for you. pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(image)

Show the extracted text

extracted_textThe image contains the question: "Which number line represents the solution to $|3x - 3| < 3$?"

From the text, there are several options with number lines labeled with various values, but unfortunately, the details of each option are unclear due to the image quality.

To solve the problem:

Step-by-Step Solution:

We need to solve the inequality $|3x - 3| < 3$.

1. Rewrite the absolute value inequality: $|3x - 3| < 3$ This can be rewritten as a compound inequality: $-3 < 3x - 3 < 3$

2. Solve for $x$:

   • Add 3 to all parts of the inequality: $0 < 3x < 6$
   • Divide by 3: $0 < x < 2$

Thus, the solution to the inequality is $0 < x < 2$, meaning that $x$ lies between 0 and 2.

Next Steps:

If you have access to the number lines in your image, you should look for the one that shows this interval: between 0 and 2.

Would you like me to assist you further with interpreting the options or provide more details on the topic? Let me know if you'd like a more thorough explanation!

Here are 5 follow-up questions:

1. How can you graph the solution $0 < x < 2$ on a number line?
2. What does the notation $|3x - 3|$ mean in absolute value problems?
3. How do you solve absolute value inequalities with different symbols, like $\leq$ or $\geq$?
4. What is the general process to solve any absolute value inequality?
5. How would this inequality change if the sign was reversed to $|3x - 3| > 3$?

Tip: When solving absolute value inequalities, always remember to break it into two cases: one for the positive and one for the negative value inside the absolute value expression!