To solve this problem, we need to establish an algebraic equation based on the given information and solve for the positive integer.
### Problem Statement:
The sum of 5 less than 3 times a positive integer and 2 times the same positive integer is equal to 20. We need to find the value of the positive integer.
### Step-by-Step Solution:
1. Define the Positive Integer: Let the positive integer be [tex]\( x \)[/tex].
2. Formulate the Expression:
- 3 times the positive integer is [tex]\( 3x \)[/tex].
- 5 less than [tex]\( 3x \)[/tex] is [tex]\( 3x - 5 \)[/tex].
- 2 times the positive integer is [tex]\( 2x \)[/tex].
3. Construct the Equation:
According to the problem, the sum of 5 less than 3 times the integer and 2 times the integer equals 20. This gives us:
[tex]\[
(3x - 5) + 2x = 20
\][/tex]
4. Simplify the Equation:
Combine like terms:
[tex]\[
3x - 5 + 2x = 20
\][/tex]
[tex]\[
5x - 5 = 20
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], first add 5 to both sides of the equation:
[tex]\[
5x - 5 + 5 = 20 + 5
\][/tex]
[tex]\[
5x = 25
\][/tex]
Next, divide both sides by 5:
[tex]\[
x = \frac{25}{5}
\][/tex]
[tex]\[
x = 5
\][/tex]
### Conclusion:
The positive integer that satisfies the given condition is [tex]\( x = 5 \)[/tex].
Therefore, the value of the positive integer is:
[tex]\[
\boxed{5}
\][/tex]
