We want to find the value of $X$ in the given situation.
To pass the algebra test, you must score at least $80\%$.
This means that you can miss at most $20\%$ of the problems.
To find the greatest number you can miss and still pass, we need to determine $20\%$ of the total number of problems, which is $X$.
$20\%$ of $X$ can be calculated as:
$0.20X$
Given that the greatest number you can miss is 7, we can write:
$0.20X = 7$
To solve for $X$, we can divide both sides of the equation by $0.20$:
$\frac{0.20X}{0.20} = \frac{7}{0.20}$
Simplifying, we have:
$X = 35$
The value of X is 35.
The answer is: 35
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
At Academic Academy, to pass an algebra test you must score at least $80\%$. If there are X problems on the test, what is the greatest number you can miss and still pass?
If we know the answer to the above question is 7, what is the value of unknown variable X?

### Answer:
