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The equation provided is:

\[
-0.75x + 1 = 0.5x - 3.42
\]

Let's solve for \( x \).

1. First, move the \( x \) terms to one side by adding \( 0.75x \) to both sides of the equation:

\[
1 = 0.5x + 0.75x - 3.42
\]

This simplifies to:

\[
1 = 1.25x - 3.42
\]

2. Next, isolate \( x \) by adding \( 3.42 \) to both sides:

\[
1 + 3.42 = 1.25x
\]

This simplifies to:

\[
4.42 = 1.25x
\]

3. Finally, divide both sides by \( 1.25 \) to solve for \( x \):

\[
x = \frac{4.42}{1.25} = 3.536
\]

So, \( x = 3.536 \).

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What happens if you solve a similar equation with different coefficients?
2. How do you solve a linear equation when the coefficient of \( x \) is zero?
3. How does the solution change if one of the terms is a fraction?
4. What is the process to verify the solution of the equation?
5. Can this method be applied to equations with variables on both sides involving more complex expressions?
6. How would you solve an equation if the terms involved radicals?
7. How can you graphically represent the solution of a linear equation?
8. How would the solution change if the equation was quadratic instead of linear?

**Tip:** When solving equations, always check your final answer by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation -0.75x + 1 = 0.5x - 3.42 step-by-step with detailed explanations and calculations. This problem covers fundamental algebraic concepts related to linear equations and variable manipulation. Suitable for high school students.

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