https://file.aiquickdraw.com/mathbot/file/1726246059746c8ll4r8q.jpg

The inequality problem in the image is:

\[
(x - 1)^2 - (x - 2)^2 > 2x - 4
\]

Let's solve this step by step.

### Step 1: Expand both sides of the inequality

First, expand the squares on the left-hand side:

\[
(x - 1)^2 = x^2 - 2x + 1
\]
\[
(x - 2)^2 = x^2 - 4x + 4
\]

So the inequality becomes:

\[
(x^2 - 2x + 1) - (x^2 - 4x + 4) > 2x - 4
\]

### Step 2: Simplify the left-hand side

Now, subtract the expressions:

\[
x^2 - 2x + 1 - (x^2 - 4x + 4) = x^2 - 2x + 1 - x^2 + 4x - 4
\]

Simplifying further:

\[
-2x + 4x + 1 - 4 = 2x - 3
\]

Now, the inequality becomes:

\[
2x - 3 > 2x - 4
\]

### Step 3: Simplify the inequality

Subtract \(2x\) from both sides:

\[
-3 > -4
\]

This is always true, because \(-3\) is indeed greater than \(-4\).

### Conclusion:

The inequality is always true, so the solution is that \(x\) can be any real number.

---

Do you want more details or have any questions?

Here are five related questions:
1. How do you handle inequalities with higher powers?
2. What are the steps to solve quadratic inequalities?
3. Can you explain how to solve absolute value inequalities?
4. What is the difference between strict inequalities and non-strict inequalities?
5. How do inequalities change when multiplied or divided by negative numbers?

**Tip:** Always remember that reversing the inequality sign is necessary when multiplying or dividing both sides by a negative number.

Learn how to solve the inequality (x - 1)^2 - (x - 2)^2 > 2x - 4 with a detailed step-by-step approach. This problem involves expanding squares, simplifying expressions, and understanding inequality properties. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation