Answer:
![x=13](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zvtwmwx4shq7mja72ckbvcxnqshnv4u71p.png)
Explanation:
The perimeter of a rectangle is given by the formula:
![P=2l+2w](https://img.qammunity.org/2021/formulas/mathematics/middle-school/etogfgv8l3noodrpi9g5odp43pg0p9l5i8.png)
Where l is the length and w is the width.
We know that the perimeter is 80. Looking at the rectangle, we can also see that the length is 2x+3 while the width is x-2. Thus, make the substitutions:
![P=2l+2w\\80=2(2x+3)+2(x-2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/q5mvgv9mt4gagwffjion89sorgs5fuu1eo.png)
Distribute:
![80=4x+6+2x-4](https://img.qammunity.org/2021/formulas/mathematics/high-school/ovyvwte4mwcn47iw5m4nv4flz7bz45jrjs.png)
Combine like terms and add:
![80=6x+2](https://img.qammunity.org/2021/formulas/mathematics/high-school/22f20sjm5px8z8lrkgd2f3fpm9wppu3280.png)
Subtract 2 from both sides:
![78=6x](https://img.qammunity.org/2021/formulas/mathematics/high-school/obxief6hgda3k1q2ggt4jz3a20k7plour2.png)
Divide both side by 6:
![x=13](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zvtwmwx4shq7mja72ckbvcxnqshnv4u71p.png)
Thus, the value of x is 13.