Answer:
![x=10](https://img.qammunity.org/2021/formulas/mathematics/middle-school/yveq4wkntm80fiuxnqfce6qwd476ocdd80.png)
Explanation:
The perimeter of a rectangle is given by the formula:
![P=2w+2l](https://img.qammunity.org/2021/formulas/mathematics/college/4nkglpccbtnid4bq4yslzwmwcgeee7an3p.png)
Where w is the width and l is the length.
The width is 4x and the length is 5x+2.
We also know the perimeter is 184. So, substitute:
![184=2(4x)+2(5x+2)](https://img.qammunity.org/2021/formulas/mathematics/college/4s8tb2d0m40kw887q7uwqkeyceep8imek8.png)
Distribute:
![184=8x+10x+4](https://img.qammunity.org/2021/formulas/mathematics/college/uqx3k7tsgw1bwb497bonmg9yoasrayacx2.png)
Combine like terms:
![184=18x+4](https://img.qammunity.org/2021/formulas/mathematics/college/fmcmwq98n2gnov27791uyjwa83m96clre0.png)
Subtract 4 from both sides:
![180=18x](https://img.qammunity.org/2021/formulas/mathematics/college/swj89lm7a7xuc14s80gn8zeveuiy2eltlf.png)
Divide by 18:
![x=10](https://img.qammunity.org/2021/formulas/mathematics/middle-school/yveq4wkntm80fiuxnqfce6qwd476ocdd80.png)
So, the value of x is 10
And we're done :)