To determine the farthest block Jamaal can walk to from his house, we need to understand the nature of absolute value equations and how they can be used to represent distances on a number line.
Let's break down the question:
1. Location of Jamaal's House: Jamaal lives at the 57th block of the town.
2. Maximum Distance: Jamaal is allowed to walk no more than 3 blocks in either direction from his house.
To represent this situation mathematically, we recall that absolute value equations are particularly useful for expressing distance without regard to direction (positive or negative).
The general form of an absolute value equation expressing distance is:
[tex]\[ |x - a| = b \][/tex]
Here, [tex]\( a \)[/tex] is the starting point (Jamaal's house location), and [tex]\( b \)[/tex] is the maximum distance allowed.
Given:
- [tex]\( a = 57 \)[/tex] (the block where Jamaal's house is located)
- [tex]\( b = 3 \)[/tex] (the maximum distance he can walk)
Substituting these values into the general equation, we get:
[tex]\[ |x - 57| = 3 \][/tex]
This equation indicates that the distance between any block [tex]\( x \)[/tex] and the 57th block is exactly 3 blocks.
So, the correct absolute value equation demonstrating the farthest block Jamaal is allowed to walk is:
[tex]\[ |x - 57| = 3 \][/tex]
Thus, the answer is:
[tex]\[ |x - 57| = 3 \][/tex]
