Let's solve the equation step by step:

The given equation is:

\[
-9(-3x - 1) - 3x = -39
\]

### Step 1: Distribute the \(-9\) across \((-3x - 1)\):

\[
-9 \times (-3x) + (-9) \times (-1) = 27x + 9
\]

So the equation becomes:

\[
27x + 9 - 3x = -39
\]

### Step 2: Combine like terms:
Combine \(27x\) and \(-3x\):

\[
(27x - 3x) + 9 = -39
\]

\[
24x + 9 = -39
\]

### Step 3: Subtract 9 from both sides to isolate the term with \(x\):

\[
24x = -39 - 9
\]

\[
24x = -48
\]

### Step 4: Divide both sides by 24 to solve for \(x\):

\[
x = \frac{-48}{24}
\]

\[
x = -2
\]

So, the solution is:

\[
x = -2
\]

Would you like further details on any step?

---

Here are 5 related questions to expand your understanding:
1. How would the solution change if the constant term on the right-hand side was different?
2. What happens if the distributive property is applied incorrectly in the first step?
3. Can you apply these steps to a similar equation with different coefficients?
4. How does this method compare to solving a simpler linear equation?
5. Can this approach be used for equations involving fractions?

**Tip:** Always combine like terms before isolating the variable for easier solving.

Discover how to solve the linear equation -9(-3x - 1) - 3x = -39 with a comprehensive step-by-step approach. This problem explores key algebraic techniques such as the distributive property, combining like terms, and solving linear equations. Perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation