https://file.aiquickdraw.com/mathbot/file/17248890503107seoth2v.jpg

The equation shown in the image is:

\[
-3(x - 1) + 8(x - 3) = 6x + 7 - 5x
\]

Let's solve this step by step.

### Step 1: Distribute the constants on both sides
Distribute \(-3\) and \(8\) on the left-hand side:

\[
-3(x - 1) = -3x + 3
\]
\[
8(x - 3) = 8x - 24
\]

So, the equation now becomes:

\[
-3x + 3 + 8x - 24 = 6x + 7 - 5x
\]

### Step 2: Combine like terms
First, combine like terms on the left-hand side:

\[
(-3x + 8x) + (3 - 24) = 5x - 21
\]

Now, simplify the right-hand side:

\[
6x - 5x + 7 = x + 7
\]

So the equation is now:

\[
5x - 21 = x + 7
\]

### Step 3: Isolate the variable \(x\)
Move all the terms involving \(x\) to one side and the constant terms to the other side:

\[
5x - x = 7 + 21
\]
\[
4x = 28
\]

### Step 4: Solve for \(x\)
Divide both sides by 4:

\[
x = \frac{28}{4} = 7
\]

### Solution:
The solution to the equation is \(x = 7\).

Would you like further details on this solution or have any other questions?

Here are some related questions you might consider:

1. What would happen if you changed the sign on one of the coefficients in the equation?
2. How would you solve the equation if it involved fractions instead of integers?
3. How can you check if \(x = 7\) is indeed the correct solution?
4. What does it mean graphically when we solve an equation like this?
5. How would the solution change if the right-hand side of the equation were different?

**Tip:** When solving equations, always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation -3(x - 1) + 8(x - 3) = 6x + 7 - 5x step-by-step with detailed explanations. This problem involves combining like terms and isolating variables. Suitable for high school students.

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