Gradual part resize script?

As udayk8139 has said, you should be using a loop. But it is possible to add only the x value. Vector3 Operators

Example:-

local part = script.Parent

for i=1, 10 do -- loop
    part.Size = part.Size + Vector3.new(1,0,0) -- add one to the existing vector3
    wait(0.05)
end

I hope this helps.

While a lot of the questions are correct and can be used, I would personally recommend using Vector3:Lerp. This helps achieve much smoother movement and is overall a better idea. An example of how to implement this would be:

--Assuming part is already defined
local originalSize = part.Size
local targetSize = Vector3.new(20, 1, 5)
for i = 1, 10 do
    part.Size = originalSize:Lerp(targetSize, i/10)
    wait(0.1)
end

This would smoothly transition the size of the part over the course of a second.

A way to do this is to make a variable for the x value, and add one to it in the loop.

local xValue = 20
local part = script.Parent

while wait(.5) do
    part.Size = Vector3.new(xValue, 1, 80)
    xValue = xValue + 1
end

First we define xValue as 20 and we define the part.

Then we create an Endless loop, that runs every .5 seconds. We set the xValue of the part size to that number, and add one to the number, so next time we size it, the number will be greater by 1.

If you don't want this to be an endless loop, do the following.

local xValue = 20
local part = script.Parent

while wait(.5) do
    part.Size = Vector3.new(xValue, 1, 80)
    xValue = xValue + 1

    if xValue >= 40 then -- Change 40 to the number you want the increase to stop at.
        break -- Breaks out of loop
    end 
end