https://file.aiquickdraw.com/mathbot/file/1727701191226l80f16ej.jpg

The equation in the image is:

\[
6x + 2 = 9x - 1
\]

Let's solve for \(x\):

1. Subtract \(6x\) from both sides to move all \(x\)-terms to the right side:
   \[
   2 = 9x - 6x - 1
   \]
   Simplifying:
   \[
   2 = 3x - 1
   \]

2. Add 1 to both sides to isolate the \(x\)-term:
   \[
   2 + 1 = 3x
   \]
   Simplifying:
   \[
   3 = 3x
   \]

3. Divide both sides by 3 to solve for \(x\):
   \[
   x = 1
   \]

So, the solution is \(x = 1\).

Would you like further details, or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the solution change if the equation was \(6x + 2 = 9x + 1\)?
2. What happens if both sides of an equation have fractions instead of integers?
3. How do you check if your solution to a linear equation is correct?
4. What does it mean if after solving, you get an equation like \(0 = 0\)?
5. How would you solve an equation like \(6x^2 + 2 = 9x^2 - 1\)?

**Tip**: When solving linear equations, always try to simplify both sides of the equation before isolating the variable.

What is the solution to the equation 6x + 2 = 9x - 1?

Learn how to solve the linear equation 6x + 2 = 9x - 1 step by step, using algebraic methods including the addition and division properties of equality. This problem is suitable for students in Grades 8-10.

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