To solve the equation \(-2x + 1 = 1 - \frac{1}{2}x\), we'll go through the following steps:

### Step 1: Eliminate fractions
We can eliminate the fraction by multiplying every term by 2, the denominator of \(\frac{1}{2}\):

\[
2(-2x + 1) = 2\left(1 - \frac{1}{2}x\right)
\]

This simplifies to:

\[
-4x + 2 = 2 - x
\]

### Step 2: Move all terms involving \(x\) to one side
To isolate \(x\), let's add \(4x\) to both sides:

\[
2 = 2 + 3x
\]

### Step 3: Move constant terms to the other side
Now, subtract 2 from both sides:

\[
0 = 3x
\]

### Step 4: Solve for \(x\)
To solve for \(x\), divide both sides by 3:

\[
x = 0
\]

### Solution:
The solution is \(x = 0\).

Would you like any further details or have any questions? Here are some related problems:

1. Solve \(3x + 5 = 2x + 7\).
2. Solve \(5x - 3 = 2x + 9\).
3. Solve \(-x + 4 = 2 - x\).
4. Solve \(4x - 1 = 2x + 3\).
5. Solve \(6x + 2 = 4x - 8\).

**Tip:** Always start by eliminating fractions or decimals when solving linear equations; it simplifies the process and reduces the risk of errors.

Learn how to solve the linear equation -2x + 1 = 1 - 1/2x with a detailed step-by-step solution. This problem involves eliminating fractions and applying basic algebraic principles to isolate x. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation