To determine which equation can be used to find [tex]\( w \)[/tex], the width of the rectangle, let's start by understanding the relationship provided in the problem:
- The length of the rectangle is 4 units shorter than half the width.
In mathematical terms:
[tex]\[ \text{Length} = \frac{w}{2} - 4 \][/tex]
Given that the length is 18 units:
[tex]\[ 18 = \frac{w}{2} - 4 \][/tex]
We can solve this equation step-by-step to find [tex]\( w \)[/tex]:
1. Starting from:
[tex]\[ 18 = \frac{w}{2} - 4 \][/tex]
2. To isolate [tex]\( \frac{w}{2} \)[/tex], we add 4 to both sides of the equation:
[tex]\[ 18 + 4 = \frac{w}{2} \][/tex]
3. Simplifying the left side:
[tex]\[ 22 = \frac{w}{2} \][/tex]
4. Finally, to solve for [tex]\( w \)[/tex], we multiply both sides by 2:
[tex]\[ w = 44 \][/tex]
Now, looking back at the given equations, we see that the one that matches the step we performed (adding 4 to both sides) is:
[tex]\[ 18 - 4 = \frac{w}{2} \][/tex]
Therefore, the equation that can be used to find [tex]\( w \)[/tex] is:
[tex]\[ 18 - 4 = \frac{w}{2} \][/tex]
This corresponds to option 3.
