Solve for x.
3, left parenthesis, minus, 3, x, minus, 4, right parenthesis, plus, 3, x, minus, 1, equals, minus, 1
3(−3x−4)+3x−1=
−1

Let's solve the equation step by step:

The equation is:

\[
3(-3x - 4) + 3x - 1 = -1
\]

### Step 1: Distribute the 3
Apply the distributive property to remove the parentheses.

\[
3(-3x - 4) = 3(-3x) + 3(-4) = -9x - 12
\]

Now, substitute this back into the equation:

\[
-9x - 12 + 3x - 1 = -1
\]

### Step 2: Combine like terms
Combine the \(x\) terms and the constant terms on the left-hand side:

\[
(-9x + 3x) = -6x
\]
\[
(-12 - 1) = -13
\]

So the equation becomes:

\[
-6x - 13 = -1
\]

### Step 3: Solve for \(x\)
Now, isolate \(x\).

1. Add 13 to both sides:

\[
-6x = -1 + 13
\]

\[
-6x = 12
\]

2. Divide both sides by -6:

\[
x = \frac{12}{-6}
\]

\[
x = -2
\]

### Solution:
The solution is \(x = -2\).

---

Would you like further clarification on any of the steps? 

Here are 5 related questions to explore:

1. How do you apply the distributive property?
2. What are like terms in algebra?
3. How do you solve multi-step equations?
4. What are the rules for adding and subtracting integers?
5. How do you check if your solution to an equation is correct?

**Tip:** Always simplify equations step by step to avoid errors, starting with distributing and combining like terms.

Explore the step-by-step solution to solve the linear equation 3(-3x - 4) + 3x - 1 = -1. This problem covers algebraic concepts like the distributive property and combining like terms. Suitable for students in Grades 7-9.

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