Math Problem Statement

|2x - 3| is the distance between what number and -3?

Solution

The question asks:

Given the expression 2x3|2x - 3|, which represents the distance between some number and 3-3, identify that number.

Solution:

The absolute value 2x3|2x - 3| denotes the distance between 2x32x - 3 and 0. To rephrase the question:

The distance between what number and 3-3 is represented by the expression 2x3|2x - 3|?

Since the absolute value measures the distance between two values, we are comparing the expression 2x32x - 3 and 3-3. Therefore, we can rewrite the equation as:

2x3=(2x3)(3)=2x3+3=2x|2x - 3| = |(2x - 3) - (-3)| = |2x - 3 + 3| = |2x|

Thus, the distance is between 2x2x and 3-3.

The number in question is 2x2x, as that is the value being compared to 3-3 in terms of distance.

Would you like more details or have any questions?

Follow-up questions:

  1. What is the general interpretation of absolute value in mathematics?
  2. How can we solve for xx if given a specific value for the distance?
  3. What other mathematical operations involve calculating distances between two numbers?
  4. How does this approach change if the question involved a different constant instead of 3-3?
  5. What is the relationship between absolute values and inequalities?

Tip:

Always remember that absolute values represent the distance from zero, and they are always non-negative, regardless of the input value.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value
Distance between Numbers

Formulas

|a - b| represents the distance between a and b
|2x - 3| = |(2x - 3) - (-3)| = |2x|

Theorems

Absolute Value Properties

Suitable Grade Level

Grades 7-10