Let's solve the equation \( 4x + 6 = -x + 1 \).

### Step 1: Combine like terms
First, move all the terms involving \(x\) to one side and the constants to the other side.

\[
4x + x = 1 - 6
\]

This simplifies to:

\[
5x = -5
\]

### Step 2: Solve for \(x\)
Now, divide both sides by 5 to isolate \(x\):

\[
x = \frac{-5}{5} = -1
\]

### Solution:
The solution is \( x = -1 \).

Do you want more details or have any questions?

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**Tip**: Always simplify the equation step by step, combining like terms first to make the problem easier.

Learn how to solve the linear equation 4x + 6 = -x + 1 with a detailed step-by-step explanation. This problem focuses on algebraic concepts, including combining like terms and isolating variables, and is suitable for students in Grades 6-8.

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