### Instruction: If $y = \displaystyle\frac{1}{3x+1}$, what is the value of $x$ when $y = 1$?### Response: To find the value of $x$ when $y = 1$, I need to substitute $y = 1$ into the equation and solve for $x$.
So I have $1 = \displaystyle\frac{1}{3x+1}$.
To get rid of the fraction on the right, I can multiply both sides by $3x+1$.
That gives me $3x+1 = 1$.
Now I want to isolate $x$ by subtracting $1$ from both sides.
That gives me $3x = 0$.
Then I can divide both sides by $3$ to get $x = 0$.
So the value of $x$ when $y = 1$ is $0$.