Question

What is the maximum value of the difference between twice a number and 7 if it is at most -21?

1) -14
2) -28
3) -35
4) -42

Answer 1

The maximum value of the difference between twice a number and 7 if it is at most -21 is -21.

Step-by-step explanation:

To find the maximum value of the difference between twice a number and 7, we need to determine the largest possible value for the number by applying the given constraint. The constraint states that the difference must be at most -21.

Let's solve the inequality: 2x - 7 ≤ -21. Adding 7 to both sides, we have 2x ≤ -14. Dividing both sides by 2, we get x ≤ -7.

Therefore, the maximum value of the number is -7. Plugging this value into the expression 2x - 7, we have 2(-7) - 7 = -21. So the maximum value of the difference is -21.