\( \left. \begin{array} { l } { \overline { a b } = x + 2 cm } \\ { \overline { b } c = 9 x - 1,5 cm } \\ { \overline { a } d = 2 cm } \\ { \overline { d e } = 5 cm } \end{array} \right. \)

To solve the problem, we need to analyze the given equations and relationships between the segments. Let's break down the information provided: 1. \( \overline{ab} = x + 2 \, \text{cm} \) 2. \( \overline{bc} = 9x - 1.5 \, \text{cm} \) 3. \( \overline{ad} = 2 \, \text{cm} \) 4. \( \overline{de} = 5 \, \text{cm} \) We can assume that points \( a, b, c, d, e \) are collinear, and we can express the total length of the segment \( \overline{ae} \) in terms of \( x \). The total length from point \( a \) to point \( e \) can be expressed as: \[ \overline{ae} = \overline{ad} + \overline{de} + \overline{bc} + \overline{ab} \] Substituting the known values: \[ \overline{ae} = \overline{ad} + \overline{de} + \overline{bc} + \overline{ab} = 2 \, \text{cm} + 5 \, \text{cm} + (9x - 1.5) \, \text{cm} + (x + 2) \, \text{cm} \] Now, let's simplify this expression: \[ \overline{ae} = 2 + 5 + (9x - 1.5) + (x + 2) \] \[ = 7 + 9x - 1.5 + x + 2 \] \[ = 7 + 2 - 1.5 + 10x \] \[ = 7.5 + 10x \] Now, we need to determine if there is any additional information or constraints that can help us find the value of \( x \). If we assume that \( \overline{ae} \) is a specific length, we can set up an equation. However, without additional information about the total length of \( \overline{ae} \), we cannot solve for \( x \). If you have any specific total length for \( \overline{ae} \) or any other relationships, please provide that information so we can proceed with solving for \( x \).