https://file.aiquickdraw.com/mathbot/file/1726863668074ncortouo.jpg

The equation in the image is:

\[
2(5x - 3) + 13 = 7x - 6
\]

Let's solve it step by step.

1. First, distribute the 2 on the left-hand side:

\[
2 \cdot (5x) - 2 \cdot (3) + 13 = 7x - 6
\]
\[
10x - 6 + 13 = 7x - 6
\]

2. Combine like terms:

\[
10x + 7 = 7x - 6
\]

3. Now, move all the \(x\)-terms to one side and the constants to the other side. Subtract \(7x\) from both sides:

\[
10x - 7x + 7 = -6
\]
\[
3x + 7 = -6
\]

4. Subtract 7 from both sides to isolate the term with \(x\):

\[
3x = -6 - 7
\]
\[
3x = -13
\]

5. Finally, divide both sides by 3:

\[
x = \frac{-13}{3}
\]

So, the solution is:

\[
x = \frac{-13}{3}
\]

Would you like any further explanation, or details about any specific step?

### Related Questions:
1. What are the properties of linear equations?
2. How do you check if a solution is correct?
3. How would the solution change if there was an additional variable in the equation?
4. What is the graphical representation of linear equations?
5. How do we solve systems of linear equations with two variables?

### Tip:
When solving equations, always simplify both sides of the equation before attempting to move terms around!

Learn how to solve the linear equation 2(5x - 3) + 13 = 7x - 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and properties of equality. Suitable for students in Grades 7-9.

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