How can I make a moving model, that moves alongside of X slowly?

Change the (0,0,0) in the second line to how far you want it to go, in this case you'd change the x axis. Experiment with the time to see what seems right. Change the increment to something quite low, to make it look smooth.

Basically you can make it slide along the x axis

local Part = Workspace.Part -- this is the Part we will move
local newPos = Part.Position + Vector3.new(0,0,0) -- the position the Part will go to
local Time = 10 -- the time that the script will take to move the part
local Increment = 0.5 -- the Part will move 0.5 studs each time it moves
local Debounce = false

local Diff = newPos - Part.Position -- the difference between the two positions
local Mag = Diff.magnitude -- the distance between the two parts
local Direction = CFrame.new(Part.Position, newPos).lookVector

function MovePart() -- function to move the Part
    if Debounce then return end -- end the function if debounce is true
    Debounce = true -- make Debounce true so the function can't run
    for n = 0, Mag, Increment do
        Part.CFrame = Part.CFrame + (Direction * Increment)
        wait( (Time/Mag) * Increment )
    end
    Debounce = false -- set Debounce to false so the function can run again
end

Workspace.Button.ClickDetector.MouseClick:connect(MovePart)

code source: roblox wiki part sliding