Let's solve the equation step by step.

The equation is:

\[
6.5x + 1 = x - (2x + 8.4) - 5
\]

### Step 1: Simplify the right side of the equation
Distribute the negative sign through the parentheses:

\[
6.5x + 1 = x - 2x - 8.4 - 5
\]

Now, combine like terms on the right side:

\[
6.5x + 1 = -x - 13.4
\]

### Step 2: Move all the \(x\) terms to one side of the equation
Add \(x\) to both sides to get all the \(x\) terms on the left side:

\[
6.5x + x + 1 = -13.4
\]

Simplify the left side:

\[
7.5x + 1 = -13.4
\]

### Step 3: Isolate the \(x\) term
Subtract 1 from both sides:

\[
7.5x = -14.4
\]

### Step 4: Solve for \(x\)
Divide both sides by 7.5:

\[
x = \frac{-14.4}{7.5}
\]

Simplifying the fraction:

\[
x = -1.92
\]

So, the solution is:

\[
\boxed{x = -1.92}
\]

Would you like more details or have any questions?

### Related Questions:
1. What happens if the equation includes fractions?
2. How do you solve equations with variables on both sides?
3. What is the process for solving quadratic equations?
4. Can you demonstrate solving an equation with parentheses and distribution?
5. How do you handle equations with absolute values?

**Tip:** Always check your solution by plugging it back into the original equation to verify it satisfies the equation.

Learn how to solve the linear equation 6.5x + 1 = x − (2x + 8.4) − 5 with a detailed step-by-step approach. This problem involves key algebraic concepts such as distribution, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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