Solve for \( x \) in this equation: \( |2.5 x-6.8|=12.9 \) Step 1. Rewrite the absolute value equation as two linear equations Negative case: Positive case

Solve the equation \( |2.5x-6.8|=12.9 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\left|2.5x-6.8\right|=12.9\) - step1: Simplify: \(\left|\frac{5}{2}x-\frac{34}{5}\right|=12.9\) - step2: Calculate: \(\left|\frac{5}{2}x-\frac{34}{5}\right|=\frac{129}{10}\) - step3: Separate into possible cases: \(\begin{align}&\frac{5}{2}x-\frac{34}{5}=\frac{129}{10}\\&\frac{5}{2}x-\frac{34}{5}=-\frac{129}{10}\end{align}\) - step4: Solve the equation: \(\begin{align}&x=\frac{197}{25}\\&x=-\frac{61}{25}\end{align}\) - step5: Rewrite: \(x_{1}=-\frac{61}{25},x_{2}=\frac{197}{25}\) The solutions to the equation \(|2.5x-6.8|=12.9\) are \(x=-2.44\) and \(x=7.88\).