Sure! Let's start by understanding the problem statement and translating that into a mathematical equation step-by-step.
Problem Statement:
- We know the length of the rectangle is [tex]\( 18 \)[/tex] units.
- The length of the rectangle is also described as 4 units shorter than half the width.
Let [tex]\( w \)[/tex] represent the width of the rectangle.
1. Expressing the length using width:
According to the problem, the length ([tex]\( L \)[/tex]) is 4 units shorter than half of the width ([tex]\( \frac{w}{2} \)[/tex]). This relationship can be written as:
[tex]\[
L = \frac{w}{2} - 4
\][/tex]
2. Given length:
We know that the length ([tex]\( L \)[/tex]) of the rectangle is 18 units:
[tex]\[
L = 18
\][/tex]
3. Substitute the given length into the equation:
Substitute [tex]\( L \)[/tex] with 18 in the equation from step 1:
[tex]\[
18 = \frac{w}{2} - 4
\][/tex]
This gives us the required equation to find the width ([tex]\( w \)[/tex]). Let's list all the given equations and identify which one matches our derived equation:
[tex]\[
18 = \frac{w}{2} - 4
\][/tex]
[tex]\[
18 = 4 - \frac{w}{2}
\][/tex]
[tex]\[
18 - 4 = \frac{w}{2}
\][/tex]
[tex]\[
18 - \frac{w}{2} = 4
\][/tex]
From the comparison, we can see that the first equation matches our derived equation.
Therefore, the correct equation that can be used to find the width [tex]\( w \)[/tex] is:
\[
18 = \frac{w}{2} - 4
