We can solve the equation step by step:

\[
-10x - (9x + 6) = 3 + x
\]

### Step 1: Distribute the negative sign through the parentheses:
\[
-10x - 9x - 6 = 3 + x
\]

### Step 2: Combine like terms on the left-hand side:
\[
-19x - 6 = 3 + x
\]

### Step 3: Move all terms involving \(x\) to one side by subtracting \(x\) from both sides:
\[
-19x - x - 6 = 3
\]
\[
-20x - 6 = 3
\]

### Step 4: Add 6 to both sides to move the constant to the right-hand side:
\[
-20x = 9
\]

### Step 5: Solve for \(x\) by dividing both sides by \(-20\):
\[
x = \frac{9}{-20}
\]
\[
x = -\frac{9}{20}
\]

So, the solution is:
\[
x = -\frac{9}{20}
\]

Would you like further explanation or details about the solution?

Here are 5 questions related to this:

1. How do you distribute negative signs in algebraic expressions?
2. What are like terms, and how do you combine them?
3. How do you isolate a variable in a linear equation?
4. What happens when you divide by a negative number?
5. How do you simplify fractions in algebraic solutions?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation!

Learn how to solve the linear equation -10x - (9x + 6) = 3 + x step-by-step. This detailed solution covers key algebraic concepts such as the distributive property and combining like terms, suitable 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