Let's solve the equation step by step:

\[
5(u - 5) - 7u = -17
\]

### Step 1: Distribute the 5 across \((u - 5)\)
\[
5u - 25 - 7u = -17
\]

### Step 2: Combine like terms (terms with \(u\))
\[
(5u - 7u) - 25 = -17
\]
\[
-2u - 25 = -17
\]

### Step 3: Add 25 to both sides to isolate the term with \(u\)
\[
-2u = -17 + 25
\]
\[
-2u = 8
\]

### Step 4: Divide both sides by -2 to solve for \(u\)
\[
u = \frac{8}{-2}
\]
\[
u = -4
\]

The solution is:
\[
u = -4
\]

Would you like further details on any step?

Here are some related questions for you to consider:
1. What if the equation was \(6(u - 5) - 7u = -20\)?
2. How do you solve an equation with variables on both sides?
3. Can you explain how distributing works in algebraic equations?
4. What happens if \(u = 0\) in an equation like this?
5. How would the solution change if we had a fraction involved?

**Tip:** Always double-check your work by substituting your solution back into the original equation!

Learn how to solve the linear equation 5(u - 5) - 7u = -17 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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