did you write this ) Let's use the equation to represent the situation:

(x/2) + 3 + x = 15

Step 1: Divide x by 2 to represent sharing the pencils equally between you and your friend:
x/2 + 3 + x = 15

Step 2: Combine like terms:
(3/2)x + 3 = 15

Step 3: Subtract 3 from both sides of the equation:
(3/2)x = 15 - 3
(3/2)x = 12

Step 4: Multiply both sides by 2/3 to solve for x:
x = (12 * 2) / 3
x = 8

Therefore, the original number of pencils you had in your box was 8.

b) If you wanted to have at least 20 pencils left in your box, we can set up the following inequality:

x/2 + 3 ≥ 20

Step 1: Subtract 3 from both sides of the inequality:
x/2 ≥ 17

Step 2: Multiply both sides by 2 to solve for x:
x ≥ 34

Therefore, you would have originally needed at least 34 pencils in your box.

c) The inequality we derived in part b) is:
x/2 + 3 ≥ 20

This represents that the number of pencils you originally had divided by 2, plus 3, is greater than or equal to 20.