To solve the equation \(-5x - 7 + 10x = -6\), let's go step by step:

### Step 1: Combine like terms
First, combine the \(x\)-terms on the left-hand side:

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

So the equation becomes:

\[
5x - 7 = -6
\]

### Step 2: Isolate the variable term
Next, add 7 to both sides to isolate the term with \(x\):

\[
5x - 7 + 7 = -6 + 7
\]

\[
5x = 1
\]

### Step 3: Solve for \(x\)
Now, divide both sides by 5 to solve for \(x\):

\[
x = \frac{1}{5}
\]

Thus, the solution is:

\[
x = \frac{1}{5}
\]

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you solve equations with fractions?
2. What happens if the variable appears on both sides of the equation?
3. How do you solve quadratic equations?
4. What is the difference between linear and quadratic equations?
5. How do you solve a system of linear equations?

**Tip:** Always combine like terms and simplify the equation before solving for the variable.

Learn how to solve the linear equation -5x - 7 + 10x = -6 with a detailed step-by-step solution. This problem involves key algebraic concepts like combining like terms and isolating the variable. Suitable for students in Grades 6-8.

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