Solve for x.
minus, 3, left parenthesis, 5, x, minus, 5, right parenthesis, plus, 5, x, plus, 1, equals, minus, 24
−3(5x−5)+5x+1=
−24

Let's solve the equation step by step:

Given:
\[
-3(5x - 5) + 5x + 1 = -24
\]

### Step 1: Distribute the \(-3\) across \((5x - 5)\)
\[
-3(5x) + (-3)(-5) + 5x + 1 = -24
\]
This simplifies to:
\[
-15x + 15 + 5x + 1 = -24
\]

### Step 2: Combine like terms
\[
(-15x + 5x) + (15 + 1) = -24
\]
\[
-10x + 16 = -24
\]

### Step 3: Move the constant \(16\) to the right-hand side by subtracting \(16\) from both sides
\[
-10x = -24 - 16
\]
\[
-10x = -40
\]

### Step 4: Solve for \(x\) by dividing both sides by \(-10\)
\[
x = \frac{-40}{-10}
\]
\[
x = 4
\]

Thus, the solution is:
\[
x = 4
\]

Would you like further details or clarification on any step?

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Here are 5 questions related to this problem:
1. How would the solution change if the constant on the right side was different?
2. What happens if we have a different coefficient for \(x\) in the parentheses?
3. Can you solve a similar equation with fractions?
4. How would you check if the solution \(x = 4\) is correct?
5. Can this method be applied to more complex equations with multiple parentheses?

**Tip:** Always simplify expressions inside parentheses before distributing.

Learn how to solve the linear equation −3(5x−5)+5x+1=−24 step by step. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 8-10.

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