Solve the equation  
3
x
+
2
=
−
5
x
+
1
  algebraically. Answer as a "reduced Proper or Improper" fraction only.

We are given the equation:

\[
3x + 2 = -5x + 1
\]

### Step-by-Step Solution:

1. **Move the terms involving \(x\) to one side:**
   Add \(5x\) to both sides:
   \[
   3x + 5x + 2 = 1
   \]
   This simplifies to:
   \[
   8x + 2 = 1
   \]

2. **Isolate the term with \(x\):**
   Subtract \(2\) from both sides:
   \[
   8x = 1 - 2
   \]
   This simplifies to:
   \[
   8x = -1
   \]

3. **Solve for \(x\):**
   Divide both sides by 8:
   \[
   x = \frac{-1}{8}
   \]

Thus, the solution is:

\[
x = \frac{-1}{8}
\]

This is a reduced improper fraction.

Would you like more details or have any questions?

### Related questions:
1. How do you solve equations with variables on both sides?
2. What is the process to simplify fractions?
3. How can you check if your solution to an equation is correct?
4. What does it mean to have an improper fraction?
5. Can you solve equations that include parentheses?

**Tip:** Always double-check by plugging your solution back into the original equation to verify its correctness.

Solve the equation 3x + 2 = −5x + 1 algebraically. Answer as a 'reduced Proper or Improper' fraction only.

Learn how to solve the linear equation 3x + 2 = -5x + 1 with a detailed, step-by-step solution. This problem demonstrates key algebraic concepts, including isolating variables and solving for x, and is suitable for students in Grades 6-8.

Math Problem Statement

Solve the equation
3 x + 2

Solution

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