Try It: Solving $|\frac{3}{4}x - 5| + 9 = 4$

You are a logistics coordinator reviewing a routing software's error-checking algorithm. One of the formulas simplifies to the equation $|d - 40| = -5$, where $d$ represents delivery distance variance. Recalling the fundamental rules of absolute value equations, what does this outcome indicate about the algorithm's formula?

A technician is calibrating a high-precision pressure gauge. The error-check formula for the device simplifies to the equation $|p - 80| = -3$, where $p$ represents the pressure reading. Is it true or false that there is no numerical value of $p$ that satisfies this equation?

Structural Integrity Assessment

A production manager is verifying the logic of an automated weight scale used in a packaging facility. The scale's error-checking formula simplifies to $|w - 10| + 4 = 1$. Arrange the following steps in the correct order to recall the logical process used to determine that this equation has no solution.

A quality assurance specialist is reviewing the automated pH monitoring system for a batch of medicine. The system's error-detection formula simplifies to $|p - 7.0| = -0.5$, where $p$ represents the pH level. Recalling that the absolute value of an expression represents distance and can never be negative, the specialist identifies that there are ____ solutions to this equation.