Question

a regulation soccer ball must have an internal pressure of 12.05 pounds per square inch (psi). the tolerance for this is 3.55 psi. which absolute value equation could be used to determine the minimum and maximum internal pressure allowed for a regulation soccer ball?
○ ( x - 3.55 = 12.05 )
○ ( |x - 12.05| = 3.55 )
○ ( |x + 3.55| = 12.05 )
○ ( |x + 12.05| = 3.55 )

Explanation:

Step1: Recall the absolute - value equation for tolerance

The formula for finding the minimum and maximum values using tolerance is \(|x - a|=b\), where \(a\) is the target value and \(b\) is the tolerance. Here, the target value \(a = 12.05\) (the nominal internal pressure) and the tolerance \(b = 3.55\).

Step2: Analyze each option

• Option A: \(x+12.05 = 3.55\) is a linear equation, not an absolute - value equation. It would give \(x=3.55 - 12.05=-8.5\), which is not related to finding values around \(12.05\) with a tolerance of \(3.55\).
• Option B: \(|x + 3.55|=12.05\) implies \(x+3.55=\pm12.05\). Solving \(x + 3.55=12.05\) gives \(x = 8.5\) and \(x+3.55=-12.05\) gives \(x=-15.6\), which is not about a value \(x\) around \(12.05\) with a tolerance of \(3.55\).
• Option C: \(|x - 12.05|=3.55\) is in the form \(|x - a|=b\). By the definition of absolute value, \(x-12.05=\pm3.55\). When \(x - 12.05=3.55\), \(x=12.05 + 3.55 = 15.6\); when \(x-12.05=-3.55\), \(x=12.05-3.55 = 8.5\). This equation can be used to find the minimum (\(8.5\)) and maximum (\(15.6\)) internal pressures.
• Option D: \(x - 3.55=12.05\) is a linear equation. Solving for \(x\) gives \(x=12.05 + 3.55=15.6\), but it does not account for the lower - bound value.

Answer:

C. \(|x - 12.05| = 3.55\)