Amy is building a house. The basement floor is at -15 feet. The roof of the house is above the ground 25 feet. Express the comparison of heights as an inequality. Explain the meaning of the inequality.
-15 < 25
To express the comparison of heights as an inequality, we can use the concept of a number line. We can assign a reference point on the number line, such as zero, to represent the ground level.
Now, let's denote the basement floor at -15 feet, which means it is located 15 feet below the reference point (the ground level at zero). We can represent this as:
Basement floor ≤ 0
Next, let's represent the roof of the house, which is 25 feet above the ground level (zero). We can represent this as:
Roof > 0
Combining these two expressions, we get:
-15 ≤ 0 < 25
This inequality essentially states that the basement floor (at -15 feet) is less than or equal to the ground level (represented as zero), and the roof of the house (at 25 feet) is above the ground level (represented as zero).
In other words, the inequality implies that the basement floor is below the ground level, while the roof is above the ground level.