Question

the weight of an object on a particular scale is 175.2 lbs. the measured weight may vary from the actual weight by at most 0.1 lbs. what is the range of actual weights of the object? a. $175.1 \leq x \leq 175.3$ b. $x \leq 175.1$ or $x \geq 175.3$ c. $175.1 \geq x \leq 175.3$ d. $175.1 \geq x \geq 175.3$

Explanation:

Step1: Define the inequality

Let \( x \) be the actual weight. The measured weight is \( 175.2 \) lbs and the variation is at most \( 0.1 \) lbs. So, the absolute difference between the measured weight and actual weight is \( |x - 175.2| \leq 0.1 \).

Step2: Solve the absolute inequality

For \( |a| \leq b \) (where \( b\geq0 \)), it is equivalent to \( -b \leq a \leq b \). So, \( - 0.1\leq x - 175.2\leq0.1 \).

Step3: Add 175.2 to all parts

Adding \( 175.2 \) to each part of the inequality: \( 175.2- 0.1\leq x\leq175.2 + 0.1 \), which simplifies to \( 175.1\leq x\leq175.3 \).

Answer:

A. \( 175.1 \leq x \leq 175.3 \)