A lifeguard station is 6 meters higher than the shore of a lake. The bottom of the lake is 12 meters below the lake’s shore. On a number line, let 0 represent the elevation of the lake’s shore, with higher elevations on the positive side of 0.
Which number sentence correctly compares the absolute values of the elevation of the lifeguard station and the bottom of the lake?
|6| < |-12|
To compare the absolute values of the elevation of the lifeguard station and the bottom of the lake, we need to consider their distances from the lake's shore.
Given:
Elevation of lifeguard station = +6 meters (higher than the shore)
Elevation of bottom of the lake = -12 meters (below the shore)
To find the absolute values, we ignore the positive/negative signs and only consider the magnitudes of the numbers.
The absolute value of +6 is simply 6.
The absolute value of -12 is 12.
Comparing the absolute values, we can say that the 12 is greater than 6.
Therefore, the correct number sentence would be:
| -12 | > | 6 |
Note: The absolute value symbols (| |) indicate that we only consider the magnitudes/absolute values of the numbers.