https://file.aiquickdraw.com/mathbot/file/172618079067292p2pw2j.jpg

Let's solve the equation from the image step by step.

The equation is:

\[
x - 1 + 2x = x + 7 + 6x
\]

### Step 1: Combine like terms on each side of the equation.

- On the left-hand side: \( x + 2x - 1 = 3x - 1 \)
- On the right-hand side: \( x + 6x + 7 = 7x + 7 \)

Now the equation becomes:

\[
3x - 1 = 7x + 7
\]

### Step 2: Move all terms involving \(x\) to one side and constant terms to the other side.

- Subtract \(3x\) from both sides:
  \[
  -1 = 7x - 3x + 7
  \]
  Which simplifies to:
  \[
  -1 = 4x + 7
  \]

- Subtract 7 from both sides:
  \[
  -1 - 7 = 4x
  \]
  Simplifying this:
  \[
  -8 = 4x
  \]

### Step 3: Solve for \(x\).

- Divide both sides by 4:
  \[
  x = \frac{-8}{4} = -2
  \]

### Solution:
The value of \(x\) is \( \boxed{-2} \).

Would you like more details on any step or have further questions?

Here are 5 related questions for practice:
1. Solve \(2x + 3 = 4x - 5\).
2. If \(x - 3 = 7x + 1\), what is the value of \(x\)?
3. Simplify and solve \(5x - 2 + 3x = 4x + 6 + 2x\).
4. How do you solve \(3(x + 4) = 2x + 9\)?
5. What happens when you have no solution in linear equations?

**Tip:** Always combine like terms first before trying to move terms across the equation!

Solve the equation: x - 1 + 2x = x + 7 + 6x

Learn how to solve the linear equation x - 1 + 2x = x + 7 + 6x with a detailed step-by-step solution. This problem covers essential algebraic concepts such as combining like terms and solving for variables. Suitable for students in Grades 7-9.

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