Question

The situation describes an overweight German Shepherd losing weight at a rate of 1.2 pounds per week. The inequality that represents this situation is:

105−1.2w≤82
This inequality represents the dog's weight decreasing by 1.2 pounds per week until it reaches the healthy weight of 82 pounds.

Answer 1

The inequality 105−1.2w≤82 represents the situation of an overweight German Shepherd losing weight at a rate of 1.2 pounds per week until it reaches the healthy weight of 82 pounds. To solve the inequality, subtract 105 from both sides, simplify, divide by -1.2, and simplify again. The solution is w ≥ 19.17.

Step-by-step explanation:

The subject of the question is Mathematics, specifically algebra. The inequality 105−1.2w≤82 represents the situation of an overweight German Shepherd losing weight at a rate of 1.2 pounds per week until it reaches the healthy weight of 82 pounds. To solve the inequality, we need to isolate the variable w. Here are the steps to solve it:

1. Subtract 105 from both sides: 105 - 105 - 1.2w ≤ 82 - 105
2. Simplify: -1.2w ≤ -23
3. Divide both sides by -1.2 (note: dividing by a negative number flips the inequality): -1.2w / -1.2 ≥ -23 / -1.2
4. Simplify: w ≥ 19.17

Therefore, the solution to the inequality is w ≥ 19.17. This means that the dog's weight must be 19.17 pounds or higher in order for it to lose weight at a rate of 1.2 pounds per week until reaching 82 pounds.