Lourdes plans to jog at least 1.5 miles. Write and solve an inequality to find x, the number of hours Lourdes will have to jog.

To solve this problem, let's break it down into steps:

1. Suppose Lourdes jogs at a rate of **r** miles per hour.
2. She plans to jog at least 1.5 miles.
3. Let **x** be the number of hours Lourdes will jog.

We can set up the inequality based on the fact that the distance jogged is equal to the rate times the time. Since she plans to jog **at least** 1.5 miles, the distance must be **greater than or equal to 1.5 miles**.

### Inequality:

\[
r \cdot x \geq 1.5
\]

Where:
- **r** is her jogging rate (miles per hour).
- **x** is the time in hours.

### Solve for \(x\):

To find **x**, solve the inequality:

\[
x \geq \frac{1.5}{r}
\]

This means the number of hours Lourdes needs to jog depends on her jogging rate. If we know her jogging rate, we can compute the exact value for \(x\).

### Example:
If Lourdes jogs at a rate of 3 miles per hour, the inequality becomes:

\[
3x \geq 1.5
\]

Solving for \(x\):

\[
x \geq \frac{1.5}{3} = 0.5 \text{ hours}
\]

So, Lourdes would need to jog at least 0.5 hours (30 minutes) to cover 1.5 miles.

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Would you like more details on solving inequalities or examples with different rates?

Here are 5 related questions to expand on this:
1. What if Lourdes jogs at a slower pace, such as 2 miles per hour?
2. How would the inequality change if she planned to jog at least 3 miles?
3. How do you graph this inequality on a number line?
4. What if the inequality stated "at most 1.5 miles" instead of "at least"?
5. Can this inequality apply to other activities like cycling or swimming?

**Tip:** When solving inequalities, always be mindful of reversing the inequality sign when multiplying or dividing by negative numbers.

Learn how to write and solve an inequality to determine how long Lourdes needs to jog to cover at least 1.5 miles. This example explores inequalities and the distance-rate-time relationship, ideal for students in Grades 6-8.

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