Let's solve the equation step by step:

Given:
\[
3(x - 5) - 5x = -25 + 6x
\]

### Step 1: Distribute the 3 on the left side.
\[
3x - 15 - 5x = -25 + 6x
\]

### Step 2: Combine like terms on the left side.
\[
(3x - 5x) - 15 = -25 + 6x
\]
\[
-2x - 15 = -25 + 6x
\]

### Step 3: Move all terms involving \(x\) to one side and constants to the other.
\[
-2x - 6x = -25 + 15
\]
\[
-8x = -10
\]

### Step 4: Solve for \(x\).
\[
x = \frac{-10}{-8} = \frac{5}{4}
\]

Thus, the solution is:
\[
x = \frac{5}{4}
\]

Would you like more details or have any other questions?

Here are 5 related questions for you to consider:
1. What happens if you change the equation to \(3(x - 5) - 6x = -25 + 7x\)?
2. How would you solve the equation if fractions were involved, such as \( \frac{1}{2}(x - 3) - 5x = -10 + \frac{1}{4}x \)?
3. Can you graph both sides of the equation \( 3(x - 5) - 5x \) and \( -25 + 6x \)? What do you notice?
4. How would you check if your solution \(x = \frac{5}{4}\) is correct?
5. Can you generalize the steps for solving linear equations of the form \( ax + b = cx + d \)?

**Tip:** Always combine like terms first to simplify the equation before isolating the variable.

Learn how to solve the linear equation 3(x-5)-5x=-25+6x with a clear step-by-step guide. This solution covers essential algebraic techniques such as distributing, combining like terms, and isolating variables. Ideal for students in Grades 7-9.

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