Questions: (x-500) / 14 > 2.95

(x-500) / 14 > 2.95
Transcript text: $\left|\frac{x-500}{14}\right|>2.95$
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Solution

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Solution Steps

To solve the inequality \(\left|\frac{x-500}{14}\right|>2.95\), we need to consider the definition of absolute value. The inequality \(|A| > B\) implies that \(A > B\) or \(A < -B\). Therefore, we will split the inequality into two separate inequalities: \(\frac{x-500}{14} > 2.95\) and \(\frac{x-500}{14} < -2.95\). We will solve each inequality for \(x\).

Step 1: Solve the First Inequality

We start with the inequality \(\frac{x-500}{14} > 2.95\). Multiplying both sides by \(14\) gives: \[ x - 500 > 2.95 \times 14 \] Calculating \(2.95 \times 14\) results in: \[ x - 500 > 41.3 \] Adding \(500\) to both sides, we find: \[ x > 541.3 \]

Step 2: Solve the Second Inequality

Next, we consider the inequality \(\frac{x-500}{14} < -2.95\). Again, multiplying both sides by \(14\) yields: \[ x - 500 < -2.95 \times 14 \] Calculating \(-2.95 \times 14\) gives: \[ x - 500 < -41.3 \] Adding \(500\) to both sides results in: \[ x < 458.7 \]

Step 3: Combine the Results

The solutions from the two inequalities are:

  1. \(x < 458.7\)
  2. \(x > 541.3\)

Final Answer

The complete solution to the inequality \(\left|\frac{x-500}{14}\right|>2.95\) is: \[ \boxed{x < 458.7 \text{ or } x > 541.3} \]

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