Let's solve the equation step by step:

Given equation:
\[
2x - 6x - 1 = 5 - 2x
\]

### Step 1: Combine like terms on the left side
\[
(2x - 6x) - 1 = -4x - 1
\]
So, the equation simplifies to:
\[
-4x - 1 = 5 - 2x
\]

### Step 2: Add \(2x\) to both sides to move the \(x\) terms to one side:
\[
-4x + 2x - 1 = 5 - 2x + 2x
\]
This simplifies to:
\[
-2x - 1 = 5
\]

### Step 3: Add 1 to both sides to isolate the term with \(x\):
\[
-2x - 1 + 1 = 5 + 1
\]
\[
-2x = 6
\]

### Step 4: Divide both sides by \(-2\) to solve for \(x\):
\[
x = \frac{6}{-2} = -3
\]

So, the solution is:
\[
\boxed{-3}
\]

Would you like more details on any of these steps or have any questions?

Here are 5 related questions:
1. How would the solution change if the constant on the right side were different?
2. Can you verify the solution by substituting \(x = -3\) back into the original equation?
3. What if the equation had a squared term, such as \(2x^2 - 6x - 1 = 5 - 2x\)?
4. How do the steps differ if the equation had fractions?
5. How would you solve the equation if the \(x\) terms were on both sides but with different coefficients?

**Tip:** Always check your solution by substituting it back into the original equation. This helps to confirm that your answer is correct.

Learn how to solve the linear equation 2x - 6x - 1 = 5 - 2x with a step-by-step solution. This problem focuses on key algebraic concepts, including combining like terms and isolating variables. Ideal 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