Essay

Irrigation Valve Calibration Guide

A community-supported agriculture (CSA) cooperative is designing a new automated irrigation system. A technician has determined that the pressure-regulating valve's ideal calibration settings, represented by the ratio pp, must satisfy the equilibrium equation (4p+3)(4p3)=0(4p + 3)(4p - 3) = 0. A newly hired assistant does not know how to solve this equation.

Write a short instructional response explaining how to solve this equation. In your explanation, you must recall and state:

  1. The mathematical property used to solve a polynomial equation when a product of factors is equal to zero.
  2. The two distinct linear equations that are created when applying this property to (4p+3)(4p3)=0(4p + 3)(4p - 3) = 0.
  3. The two solved values for pp.
  4. The exact substitution steps to verify that one of your solved values (either p=34p = -\frac{3}{4} or p=34p = \frac{3}{4}) makes the original equation true.

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Updated 2026-06-03

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