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Solve each problem by writing an inequality and solving it

To solve this problem, let's first define the variables and form the inequality.

**Given:**
- Keith's dog weighs 90 pounds.
- A healthy weight for the dog is less than 75 pounds.
- The dog loses 1.25 pounds per week.

We want to find out how many weeks it will take until the dog's weight is at a healthy level (less than 75 pounds).

### Step 1: Define the variable
Let \( x \) represent the number of weeks the dog is on the diet.

### Step 2: Form the inequality
The dog's weight starts at 90 pounds and decreases by 1.25 pounds per week, so the weight after \( x \) weeks is:
\[
90 - 1.25x
\]
We want this weight to be less than 75 pounds:
\[
90 - 1.25x < 75
\]

### Step 3: Solve the inequality
Now, solve for \( x \):

1. Subtract 90 from both sides:
   \[
   -1.25x < 75 - 90
   \]
   \[
   -1.25x < -15
   \]

2. Divide both sides by -1.25, and remember to reverse the inequality since we are dividing by a negative number:
   \[
   x > \frac{-15}{-1.25}
   \]
   \[
   x > 12
   \]

### Conclusion:
It will take more than 12 weeks for Keith's dog to reach a healthy weight. So, after 13 weeks or more, the dog will be at a healthy weight.

---

Would you like more details on this solution, or have any questions?

Here are five related questions you can explore:
1. What happens if the dog loses weight at a different rate, say 1 pound per week?
2. How many weeks would it take if the target weight was 70 pounds instead of 75 pounds?
3. What if the dog starts at 85 pounds—how would that change the solution?
4. Can we write an equation instead of an inequality to model when the dog reaches exactly 75 pounds?
5. What is the percentage of weight loss after 12 weeks?

**Tip:** When solving inequalities, remember to reverse the inequality sign when multiplying or dividing by a negative number.

Keith's dog weighs 90 pounds. A healthy dog for this type should weigh less than 75 pounds. If Keith's dog can lose an average of 1.25 pounds per week on a diet, how many weeks will it take until the dog is at a healthy weight?

Solve the inequality to find out how many weeks it will take for Keith's dog to reach a healthy weight. The dog starts at 90 pounds and loses 1.25 pounds per week. This problem covers algebraic concepts related to solving linear inequalities, suitable for students in Grades 6-8.

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