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I am trying to make the background of a drawing transparent, yet the drawing is a little bit blurry giving some problems. The drawing is only black and white, and I am trying to get all the white removed. I believe the best way is to get each pixel to be black, yet having the opacity be such that when placed in front of a white background, it looks just like the original drawing. This should achieve how the drawing would have looked like if he had drawn with a clear background in the first place (yet his drawing program doesn't have clear backgrounds, which is why he asked me cuz I have photoshop, and I thought it'd be easier than I thought).

I tried to use the magic eraser and select color range (where the color was white) and neither gave me what I want. They both treat the grey from the blurriness as a grey and only sometimes simply erasing it.

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Make a solid black layer. Insert a layer mask to it.

Copy your black on white drawing to the layer mask. Invert the mask. Now the black areas in the original drawing make a part of the solid black visible, white parts of the original drawing cause transparency.

You get the layer mask onscreen by clicking the mask icon in the layers panel and holding Alt key at the same time. Then you can paste in place what you have in the clipboard. Copy the drawing to there before you insert the layer mask.

You can invert the drawing as well before or after copying it to the layer mask. Click the image icon in the layers panel to see the result. Close or remove the layer which has the original drawing.

If your white wasn't full white or black wasn't full black, the transparency or opacity aren't 100%. You may need to apply Curves to the layer mask. Select the mask icon in the layers panel for it.

An example:

enter image description here

Your writing is as white on black (=inverted) in the layer mask of a solid black layer. As you see the writing is slightly transparent. That's because the screenshot has a little grey text. The curves applied to the mask will fix it:

enter image description here

The image can be saved as PSD or PNG and the transparency stays.

If the transparent background was needed to make inserting another background than white possible, you can as well use layer blending to mix the drawing and the new background:

enter image description here

Here a piece of your text has blending mode Multiply. The background image has blending mode Normal.

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