Question

During a recent visit to the veterinarian’s office, Mrs. Vasquez was informed that a healthy weight for her cat is approximately 10 pounds, plus or minus one pound. Write an absolute value inequality that represents unhealthy weights w for her cat.

Answer 1

The given healthy weight range for Mrs. Vasquez’s cat is between 9 and 11 pounds. An absolute value inequality can express the weights outside of this healthy range. In this case, we can consider the deviation of the cat’s weight w from the ideal weight of 10 pounds. The absolute value of this deviation should be more excellent than 1 pound to represent unhealthy weights. Therefore, the inequality can be written as:

`\[ |w - 10| > 1 \]`

This inequality says that the absolute value of the difference between the cat’s weight w and 10 pounds is greater than 1 pound, representing the unhealthy weight range for Mrs. Vasquez’s cat.

Answer 2

To represent unhealthy weights for Mrs. Vasquez's cat, the absolute value inequality is |w - 10| > 1.

Step-by-step explanation:

To write an absolute value inequality that represents unhealthy weights w for her cat, we need to consider the range of weights that are considered healthy. Mrs. Vasquez was informed that a healthy weight for her cat is approximately 10 pounds, plus or minus one pound. So, the healthy weight range would be from 10 - 1 = 9 pounds to 10 + 1 = 11 pounds. Any weight outside this range would be considered unhealthy.

Therefore, the absolute value inequality that represents unhealthy weights w for her cat would be |w - 10| > 1, which means the distance between w and 10 is greater than 1 pound.