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The image explains the concept of an **identity equation**, which is an equation that is true for all values of the variable. The provided examples are:

a. \( 3x + 4 = 4 + 3x \)

b. \( x(x - 3) = x^2 - 3x \)

c. \( (x + 1)^2 = x^2 + 2x + 1 \)

### Explanation:
- An **identity equation** holds true for any value of the variable, meaning the equation is valid regardless of what number is substituted into the variable.
- Each of the equations listed can be simplified to show that both sides are equivalent.

Let's verify that each example is an identity equation:

**Example a:**
\[
3x + 4 = 4 + 3x
\]
Both sides are clearly identical after rearranging the terms.

**Example b:**
\[
x(x - 3) = x^2 - 3x
\]
Expanding the left-hand side:
\[
x(x - 3) = x^2 - 3x
\]
Both sides are already identical.

**Example c:**
\[
(x + 1)^2 = x^2 + 2x + 1
\]
Expanding the left-hand side:
\[
(x + 1)^2 = (x + 1)(x + 1) = x^2 + 2x + 1
\]
Both sides are also identical.

In each case, the equation is true for all values of \(x\), confirming that these are **identity equations**.

Would you like more details on any of these examples or further explanations?

Here are some related questions for exploration:

1. What is the difference between an identity equation and a conditional equation?
2. How can you verify if an equation is an identity equation?
3. Can an identity equation have no solutions for certain values of \(x\)?
4. How does an identity equation differ from an inconsistent equation?
5. Are there any practical applications of identity equations in real-world problems?

**Tip**: When working with identity equations, it's useful to simplify both sides of the equation to confirm they are equivalent for all values of the variable.

What is an identity equation? Provide examples and explanations.

This page explains the concept of identity equations, which are equations that hold true for any value of the variable. Detailed examples, including 3x + 4 = 4 + 3x and (x + 1)^2 = x^2 + 2x + 1, are provided with explanations suitable for students in Grades 8-10.

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