Math Problem Statement

mode x-1 mode > 0

Solution

The expression you provided seems to involve the absolute value function, typically denoted as x1|x-1|. Let's interpret it as x1>0|x-1| > 0.

To solve the inequality x1>0|x-1| > 0:

  1. The absolute value x1|x-1| is defined as:

    x-1 & \text{if } x-1 \geq 0 \\ -(x-1) & \text{if } x-1 < 0 \end{cases}$$
  2. The absolute value x1|x-1| is greater than 0 if x10x-1 \neq 0. Therefore: x10x - 1 \neq 0

  3. Solving for xx: x1x \neq 1

So, the solution to the inequality x1>0|x-1| > 0 is: x1x \neq 1

Would you like more details or have any questions? Here are five questions you can ask:

  1. How do I solve absolute value equations?
  2. What is the difference between absolute value equations and inequalities?
  3. Can you provide examples of solving compound inequalities?
  4. How do I graph absolute value functions?
  5. What are some real-world applications of absolute value inequalities?

Tip: When solving absolute value inequalities, always consider the two cases (positive and negative) and combine the solutions appropriately.

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Inequalities

Formulas

Absolute Value definition: |x-1| = { x-1 if x >= 1, -(x-1) if x < 1 }

Theorems

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Suitable Grade Level

Grades 9-12