https://file.aiquickdraw.com/mathbot/file/1725891514348vzizuaoe.jpg

The equation provided in the image is:

\[
6x + 2y + 3 = 8x - 1
\]

We are asked to solve for \( x \). Let's go through the steps:

### Step 1: Move all terms involving \( x \) to one side
Subtract \( 6x \) from both sides:

\[
6x + 2y + 3 - 6x = 8x - 1 - 6x
\]

Simplifying:

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

### Step 2: Isolate \( x \)
Now, subtract 3 from both sides:

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

Simplifying:

\[
2y = 2x - 4
\]

### Step 3: Solve for \( x \)
Divide both sides by 2 to isolate \( x \):

\[
\frac{2y}{2} = \frac{2x - 4}{2}
\]

Simplifying:

\[
y = x - 2
\]

Thus, the solution for \( x \) is:

\[
x = y + 2
\]

Would you like more details on any of the steps? 

Here are 5 related questions for practice:
1. What happens if \( y = 3 \) in the final solution?
2. How would you solve this if it was instead \( 6x + 2y + 3 = 8x + 1 \)?
3. What if there was a squared term, like \( 6x^2 + 2y + 3 = 8x - 1 \)?
4. Could you solve this equation using substitution if another equation for \( y \) was given?
5. How would you graph the relationship between \( x \) and \( y \)?

**Tip:** Always collect like terms first when solving linear equations to simplify the process.

Solve the following for x: 6x + 2y + 3 = 8x - 1

Learn how to solve the linear equation 6x + 2y + 3 = 8x - 1 step-by-step. This problem covers key algebraic concepts such as isolating variables, combining like terms, and solving for x in linear equations. Ideal for students in Grades 8-10.

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