To solve the equation \(2(x - 1) + 3x - 5 = -17\), follow these steps:

### Step 1: Distribute and simplify
First, distribute the \(2\) across the terms inside the parentheses:

\[
2(x - 1) = 2x - 2
\]

So the equation becomes:

\[
2x - 2 + 3x - 5 = -17
\]

### Step 2: Combine like terms
Now, combine the \(x\) terms and the constant terms on the left side:

\[
(2x + 3x) + (-2 - 5) = -17
\]
\[
5x - 7 = -17
\]

### Step 3: Isolate the variable \(x\)
To solve for \(x\), first add \(7\) to both sides of the equation:

\[
5x - 7 + 7 = -17 + 7
\]
\[
5x = -10
\]

Now, divide both sides by \(5\):

\[
x = \frac{-10}{5}
\]
\[
x = -2
\]

### Final Answer
The solution to the equation is:

\[
\boxed{x = -2}
\]

Would you like further details or explanations on any part of this solution?

### Related Questions:
1. How do you solve equations with variables on both sides?
2. What is the next step if the equation has fractions?
3. How do you check if a solution is correct by substituting it back into the original equation?
4. What are the properties of equality used in solving equations?
5. How do you solve a system of linear equations?
6. Can equations always be simplified by combining like terms first?
7. How do you solve inequalities involving similar steps?
8. What happens if you get a false statement while solving an equation?

**Tip:** Always combine like terms first and simplify the equation before isolating the variable to make the solving process easier.

Learn how to solve the equation 2(x-1)+3x-5=-17 step-by-step. This problem involves equations, distributive property, combining like terms, and isolating variables. Suitable for Grades 7-9.

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