To solve the given problem, let's break it down step-by-step:
1. Understand the problem statement:
- We have a rectangle.
- The length of the rectangle is defined as 4 units shorter than half the width.
- The length of the rectangle is given as 18 units.
- We need to find an equation to determine [tex]\( w \)[/tex], the width of the rectangle.
2. Translate the statements into mathematical expressions:
- Let [tex]\( L \)[/tex] be the length of the rectangle.
- Let [tex]\( w \)[/tex] be the width of the rectangle.
- According to the problem, [tex]\( L = 18 \)[/tex].
3. Relate the length [tex]\( L \)[/tex] to the width [tex]\( w \)[/tex]:
- The problem states that the length of the rectangle is 4 units shorter than half the width.
- Mathematically, this can be expressed as:
[tex]\[
L = \frac{w}{2} - 4
\][/tex]
4. Substitute the known value into the equation:
- Substituting [tex]\( L = 18 \)[/tex] into the equation, we get:
[tex]\[
18 = \frac{w}{2} - 4
\][/tex]
5. Identify the correct equation:
- From the options given, the equation that matches our derived equation is:
[tex]\[
18 = \frac{w}{2} - 4
\][/tex]
Therefore, the correct equation to find [tex]\( w \)[/tex], the width of the rectangle, is:
[tex]\[ 18 = \frac{w}{2} - 4 \][/tex]
