Deon is inspecting a zipline at an adventure park. For safety reasons, the top platform must be 6.5 (a) Let \( x \) represent the height (in yards) of the top platform. Write an absolute value inequality platform. These heights are where the zipline will pass inspection. - \( \square \) \( \square \) \( \square \) \( \square \) - \( \square \) \( \leq \) \( \square \) \( \square \) \( + \) \( \square \) \( > \) \( \square \) \( \square \) - \( \square \) \( > \) \( \square \) (b) Solve the absolute value inequality from part (a). \( \square \) \( \square \) and \( \square \) \( \geq \square \)

To ensure the zipline passes inspection, we can define the acceptable height of the platform as being within a safe distance from the required height of 6.5 yards. Assuming we have a maximum allowable deviation of, say, 0.5 yards from that height, our absolute value inequality can be expressed as: \[ |x - 6.5| \leq 0.5 \] This means the height of the platform \( x \) must be within 0.5 yards of 6.5 yards. Now, let's find where this inequality stands. We can split the absolute value inequality into two parts. So, solving \( -0.5 \leq x - 6.5 \leq 0.5 \) gives us: 1. \( x - 6.5 \geq -0.5 \) leads to \( x \geq 6.0 \) 2. \( x - 6.5 \leq 0.5 \) leads to \( x \leq 7.0 \) Thus, the solution to the absolute value inequality is: \[ 6.0 \leq x \leq 7.0 \] So, the acceptable height range for the top platform is between 6.0 and 7.0 yards. Safety first—now the ziplines can keep soaring! Did you know that ziplines in adventure parks have a rich history? They were originally used in places like the Himalayas for transporting goods and people over difficult terrains. Modern zipline parks stem from this exciting use, providing thrills while ensuring safety and adventure! Also, if you plan to set up your own zipline, be sure to check local regulations regarding height and safety measures; they can vary widely! This ensures that your thrill-seekers have a safe and exhilarating experience.