Final answer:
The number in question is found by setting up the equation (x + 13) / -7 = -4, and solving for 'x'. Following order of operations and sign rules, we determine that the number is 15.
Step-by-step explanation:
The question asks us to find a number when given that the quotient of that number increased by 13 and -7 is -4. To solve this, we set up an equation and follow the multiplication and division rules for signs and the order of operations.
Let the unknown number be 'x'. According to the problem, (x + 13) / -7 = -4. Multiplying both sides by -7 to eliminate the denominator, we get x + 13 = (-7)(-4). Applying the rule that the product of two negative numbers is positive, we simplify the right side to get x + 13 = 28. Now, we subtract 13 from both sides to isolate 'x': x = 28 - 13, which gives us x = 15.
The number in question is therefore 15.