Given:
The area of the rectangular garden is 18z+24 sq ft.
To find the possible dimensions of the garden.
Formula
The area of the rectangular garden is

where,
l be the length of the rectangle
b be the width.
Let us take l and b be the length and width of the given rectangular park respectively.
Now,
According to the problem,

or, 
We can determine that,
l = 6 and b = 3z+4 or vice versa.
Hence,
The possible length and width of the rectangular garden is 6 and (3z+4) respectively.
Answer:
The solution is:
![-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7Dx%5Cge%20%5C%3A4%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%5Cle%20%5C%3A-8%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%2C%5C%3A-8%5D%5Cend%7Bbmatrix%7D)
The number line graph of the solution is also attached below.
From the graph, it is clear that the 2nd number line represents the solution set for the inequality.
Step-by-step explanation:
Given the inequality

Let us solve the inequality

Multiply both sides by -1 (reverse the inequality)

Simplify

Multiply both sides by 2

Simplify

Thus, the solution is:
![-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7Dx%5Cge%20%5C%3A4%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%5Cle%20%5C%3A-8%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%2C%5C%3A-8%5D%5Cend%7Bbmatrix%7D)
The number line graph of the solution is also attached below.
From the graph, it is clear that the 2nd number line represents the solution set for the inequality.