Let's solve the equation step by step:

Given equation:
\[
x - 27 = -[27 - x]
\]

1. First, distribute the negative sign on the right-hand side:
\[
x - 27 = -27 + x
\]

2. Now, subtract \(x\) from both sides to eliminate \(x\) on the right-hand side:
\[
x - x - 27 = -27 + x - x
\]
\[
-27 = -27
\]

This simplifies to \(-27 = -27\), which is a true statement and is always true regardless of the value of \(x\).

**Conclusion:**
This means that the original equation is an **identity**, and it is true for **all values of \(x\)**. There is no specific solution; any real number \(x\) satisfies the equation.

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. What does it mean for an equation to be an identity?
2. How do you solve linear equations with variables on both sides?
3. What happens if we have different coefficients for \(x\) on both sides of an equation?
4. Can you have an equation that has no solution at all?
5. How would you solve an equation where both sides are equal expressions involving \(x\)?

**Tip:** Always check your final equation after simplifying. If you get a true statement (like \(0 = 0\)), it indicates that the equation is an identity, meaning it holds for all values of the variable.

Understand how to solve the linear equation x - 27 = -[27 - x] with a detailed explanation. This problem demonstrates the concept of identities in algebra, where the equation holds true for all values of x. Suitable for students in Grades 8-10.

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