To solve the equation \( 7x + 27 = 10x - 6 \), we will follow these steps:

### Step 1: Move the terms involving \(x\) to one side.
Subtract \(7x\) from both sides to get:
\[
27 = 10x - 7x - 6
\]
This simplifies to:
\[
27 = 3x - 6
\]

### Step 2: Move the constant terms to the other side.
Add 6 to both sides:
\[
27 + 6 = 3x
\]
This simplifies to:
\[
33 = 3x
\]

### Step 3: Solve for \(x\).
Divide both sides by 3:
\[
x = \frac{33}{3} = 11
\]

So, the solution is \( x = 11 \).

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:
1. What would happen if the original equation had a negative coefficient for \(x\)?
2. How would you solve \(5x + 12 = 3x + 20\)?
3. What if \(x\) were squared, like \(7x^2 + 27 = 10x^2 - 6\)?
4. Can you solve \(7x + 27 = 10x + 5\) and find \(x\)?
5. How would the steps change if the equation had fractions, such as \( \frac{7x}{2} + 27 = 10x - 6 \)?

**Tip**: When solving linear equations, always aim to isolate the variable on one side of the equation.

Learn how to solve the linear equation 7x + 27 = 10x - 6 with this detailed solution. This problem explains algebraic concepts like moving terms and isolating variables, suitable for students in Grades 6-8.

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