### Instruction: What is the smallest integer $n$ such that $5n + 3 > -10$?### Response: I want to find the smallest value of $n$ that makes the inequality true, so I need to isolate $n$ on one side of the inequality.
To do that, I can subtract $3$ from both sides and then divide by $5$.
Subtracting $3$ from both sides gives me $5n > -13$.
Dividing both sides by $5$ gives me $n > -\frac{13}{5}$.
Now I have an inequality that shows me that $n$ has to be larger than $-\frac{13}{5}$.
But $n$ has to be an integer, so I can't use fractions or decimals.
The smallest integer that is larger than $-\frac{13}{5}$ is $-2$, since $-\frac{13}{5}$ is between $-3$ and $-2$.
So the smallest integer $n$ that satisfies the inequality is $-2$.