\( \left. \begin{array} { c } { | 2.5 x - 6.8 | = 12.9 } \\ { 2.5 x - 6.8 = - 12.9 \quad 2.5 x - 6.8 = 12.9 } \end{array} \right. \)

To solve \( | 2.5 x - 6.8 | = 12.9 \), we break it down into two cases. In the first case, we take the positive scenario: 1. \( 2.5 x - 6.8 = 12.9 \) - Adding \( 6.8 \) to both sides gives us \( 2.5 x = 12.9 + 6.8 \). - Calculate \( 12.9 + 6.8 = 19.7 \), so \( 2.5 x = 19.7 \). - Dividing both sides by \( 2.5 \) gives us \( x = \frac{19.7}{2.5} = 7.88 \). In the second case, we consider the negative scenario: 2. \( 2.5 x - 6.8 = -12.9 \) - Again, adding \( 6.8 \) to both sides gives us \( 2.5 x = -12.9 + 6.8 \). - Calculate \( -12.9 + 6.8 = -6.1 \), so \( 2.5 x = -6.1 \). - Dividing both sides by \( 2.5 \) gives us \( x = \frac{-6.1}{2.5} = -2.44 \). Thus, the solutions to the equation \( | 2.5 x - 6.8 | = 12.9 \) are \( x = 7.88 \) and \( x = -2.44 \).