Answer:
![12.95x + 4.95 \leq 75](https://img.qammunity.org/2021/formulas/mathematics/high-school/z31bbxsh5jfj9j7b8tjj9n7phmpk5efv7f.png)
Explanation:
Given
Represent number of DVDs with x
![Each\ DVD = \$12.95](https://img.qammunity.org/2021/formulas/mathematics/high-school/kj8ipw4mj4obxh8x1452v2l6za2fe136fj.png)
![Handling\ Fee = \$4.95](https://img.qammunity.org/2021/formulas/mathematics/high-school/csav7b1x86it40kti19eimyhy19yykprkd.png)
(at most)
Required
Represent as an inequality
If
![Each\ DVD = \$12.95](https://img.qammunity.org/2021/formulas/mathematics/high-school/kj8ipw4mj4obxh8x1452v2l6za2fe136fj.png)
x DVD would cost:
![x\ DVDs = 12.95 * x](https://img.qammunity.org/2021/formulas/mathematics/high-school/povebu2ku9nnph7vwms6fgy4b8lugck2y6.png)
![x\ DVDs = 12.95x](https://img.qammunity.org/2021/formulas/mathematics/high-school/h09jc2ken7kynzqjzi7c2f09rfljcifmmz.png)
So, to make an order of x DVDs, Deacon will pay for
x DVDs and Handling Fee
So:
![Payments = 12.95x + 4.95](https://img.qammunity.org/2021/formulas/mathematics/high-school/wiskhnkvz8ekyvxnx94obef5p0ayfih7rf.png)
Recall that his budget is at most $75
This implies that:
![\leq 75](https://img.qammunity.org/2021/formulas/mathematics/high-school/6r940rkcazhu1gj1z5hfh1ol86vb8hhx15.png)
So, the relationship between his payment and budget is:
![12.95x + 4.95 \leq 75](https://img.qammunity.org/2021/formulas/mathematics/high-school/z31bbxsh5jfj9j7b8tjj9n7phmpk5efv7f.png)