### Instruction: What is the least positive integer value of $x$ for which the inequality $3x > 2x+1$ is true?### Response: To solve this inequality, I want to isolate $x$ on one side of the inequality sign.
To do that, I can subtract $2x$ from both sides, which gives me $x > 1$.
Now I have a simpler inequality that tells me that $x$ has to be greater than $1$.
The question asks for the least positive integer value of $x$, so I need to find the smallest integer that is bigger than $1$.
The smallest integer that is bigger than $1$ is $2$, so that must be the answer.