Question

a yogurt company recommends that its yogurt be stored at 37 degrees fahrenheit (°f). the company states that the recommended storage temperature can vary by 3°f. the absolute value inequality shown below represents all the recommended storage temperatures (x), in degrees fahrenheit, for the yogurt. |x - 37| ≤ 3 which number line represents all the recommended storage temperatures (x), in degrees fahrenheit, for the yogurt? a recommended storage temperatures temperature (°f) b recommended storage temperatures temperature (°f) c recommended storage temperatures temperature (°f) d recommended storage temperatures temperature (°f)

Explanation:

Step1: Solve the absolute - value inequality

Given \(|x - 37|\leq3\). By the definition of absolute - value inequality \(|a|\leq b\) (\(b\geq0\)) which is equivalent to \(-b\leq a\leq b\). Here \(a=x - 37\) and \(b = 3\), so \(-3\leq x-37\leq3\).
Add 37 to all parts of the compound inequality: \(-3 + 37\leq x-37 + 37\leq3+37\).
\(34\leq x\leq40\).

Step2: Analyze the number - line representations

• In option A, the open circles at 34 and 40 mean \(x

eq34\) and \(x
eq40\), which is wrong since our solution is \(34\leq x\leq40\).

• In option B, the solid circles at 34 and 40 mean \(x\) can be 34 and 40, and the line segment between them represents all values between 34 and 40 (inclusive), which is consistent with \(34\leq x\leq40\).
• In option C, the open circles at 34 and 40 (and the arrow directions) do not match our non - strict inequality \(34\leq x\leq40\).
• In option D, the solid circles are at 34 and 40, but the line segment is not between 34 and 40 (it skips the middle part near 37), which is incorrect.

Answer:

B. Recommended Storage Temperatures with solid circles at 34 and 40 and a line segment between them on the number line.