Final answer:
To find the numbers that satisfy the condition of the given equation, we can use algebraic expressions. The numbers that satisfy the given condition are between -4 and 3, inclusive.
Step-by-step explanation:
To find the numbers that satisfy the condition of the given equation, we can use algebraic expressions.
Let's assume the number we are looking for is 'x'.
The condition states that 'three times the number, increased by one' is between -11 and 10.
So we can write the equation as 3x + 1 ≥ -11 and 3x + 1 ≤ 10.
Simplifying the inequalities, we get x ≥ -4 and x ≤ 3.
Therefore, the numbers that satisfy the given condition are between -4 and 3, inclusive.