Let's solve the equation step by step.

The equation is:

\[
1 = 0.1x - 0.7x - 29
\]

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

\[
0.1x - 0.7x = -0.6x
\]

So, the equation becomes:

\[
1 = -0.6x - 29
\]

### Step 2: Isolate the term with \(x\)
To isolate the \(x\) term, add 29 to both sides of the equation:

\[
1 + 29 = -0.6x
\]

\[
30 = -0.6x
\]

### Step 3: Solve for \(x\)
Now, divide both sides by \(-0.6\) to solve for \(x\):

\[
x = \frac{30}{-0.6}
\]

\[
x = -50
\]

### Final Answer:
The solution to the equation is \(x = -50\).

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would you solve a similar equation if the coefficients were fractions?
2. What happens if both sides of the equation include variables?
3. Can you graphically interpret this solution on a number line?
4. How does the solution change if you change the constant term?
5. What are the steps to check the solution of this equation?
6. How would you solve this equation if the coefficients were negative?
7. How do you solve an equation where \(x\) appears on both sides?
8. Can this method be applied to quadratic equations?

**Tip:** Always double-check your calculations, especially when combining like terms and solving for variables!

Learn how to solve the equation 1 = 0.1x - 0.7x - 29 with a detailed step-by-step solution. This problem involves linear equations and requires combining like terms and isolating the variable. Suitable for students in Grades 7-9.

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