Solve for xx:
minus, 2, x, plus, 1, equals, minus, x, plus, 7
−2x+1=
−x+7

We are given the equation:

\[
-2x + 1 = -x + 7
\]

### Step 1: Get all the \( x \)-terms on one side.
First, we want to eliminate the \( -x \) on the right side. To do that, add \( x \) to both sides of the equation:

\[
-2x + 1 + x = -x + 7 + x
\]

This simplifies to:

\[
- x + 1 = 7
\]

### Step 2: Move the constant term to the other side.
Now, subtract 1 from both sides:

\[
- x + 1 - 1 = 7 - 1
\]

Simplifying gives:

\[
- x = 6
\]

### Step 3: Solve for \( x \).
To isolate \( x \), multiply both sides of the equation by \( -1 \):

\[
x = -6
\]

### Final Answer:
\[
x = -6
\]

Let me know if you need further clarification or a breakdown of any step!

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**Related Questions:**
1. How would the solution change if we had \( 2x + 1 = -x + 7 \)?
2. What is the solution to the equation \( 3x - 5 = 2x + 4 \)?
3. How do you solve an equation with fractions, like \( \frac{1}{2}x + 3 = 5 \)?
4. Can you solve equations where the variable appears on both sides, like \( 4x - 3 = 2x + 5 \)?
5. What is the difference between solving a linear equation and a quadratic equation?

**Tip:** When solving linear equations, always aim to get the variable on one side and constants on the other to simplify the process.

Learn how to solve the linear equation -2x + 1 = -x + 7 with a step-by-step breakdown. This solution covers the essential algebraic methods for isolating the variable and solving for x. Ideal for students in Grades 7-9.

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