Math Problem Statement

Simplify the expression |-3(x - 2)|.

Solution

from PIL import Image import pytesseract

Load the image from the user's upload

image_path = "/mnt/data/1732373847060o9fwtvpb.jpg" image = Image.open(image_path)

Use OCR to extract the text from the image

extracted_text = pytesseract.image_to_string(image) extracted_text'ja 3 :\n''ja 3 :\n'successThe OCR output from the image appears unclear. However, the visible part of the mathematical expression seems to involve an absolute value function, such as:

3(x2)|-3(x - 2)|

If this interpretation is correct, here's how to simplify it:

  1. Recognize the absolute value: 3(x2)|-3(x-2)|
  2. Factorize the absolute value as the product of constants and variables:

[ |-3(x - 2)|$$

If so, here's how to approach solving or simplifying it:

Simplification Steps:

  1. Absolute Value Rule: The absolute value of a product is the product of the absolute values: 3(x2)=3x2|-3(x - 2)| = |-3| \cdot |x - 2|

  2. Simplify Constant: The absolute value of 3-3 is 33, so: 3(x2)=3x2|-3(x - 2)| = 3 \cdot |x - 2|

Thus, the expression simplifies to: 3x23 \cdot |x - 2|

Would you like me to assist further or explore possible equations based on this?

Follow-Up Questions:

  1. What value of xx satisfies the equation if it equals a given number (e.g., 3(x2)=k|-3(x-2)| = k)?
  2. How does the graph of 3x23|x-2| look like?
  3. What are the critical points or intervals of increase/decrease for this function?
  4. What happens to the value when x=2x = 2?
  5. Can this expression model any real-life scenario (e.g., distance, economics)?

Tip:

When working with absolute values, always consider the behavior of the function for both positive and negative cases of the variable within the absolute value.

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Algebra

Formulas

|a * b| = |a| * |b|

Theorems

Properties of Absolute Value

Suitable Grade Level

Grades 7-9