Fake Black Hair Color

A: You're not alone in this frustrating situation, and the good news is that there are several solutions to help you achieve a more natural-looking hair color while addressing the specific challenges you're facing.
A professional hair colorist would be your best bet for achieving the natural color you want. They have access to professional-grade products and the expertise to neutralize those unwanted red tones you're seeing. Specifically, they can use a toner with a green base to counteract the redness, since green and red are opposite on the color wheel and cancel each other out. This is basic color theory that works every time when applied correctly.
If you're determined to tackle this at home, you can perform your own color correction, though it will require patience and the right products. After lightening your hair and seeing those red tones appear, you'll want to apply a light shade of hair color that has a green base - typically something at level 8 or lighter on the hair color scale. Mix this with a 10-volume developer, which is gentle enough not to cause additional damage while still allowing the color to penetrate. Apply this mixture to the reddish areas to neutralize the unwanted tones.
Another approach worth considering is transitioning to temporary or semi-permanent hair color while you let the permanent black color grow out naturally. This gives you more flexibility and allows you to experiment with different shades without the commitment. Once the permanent color has completely grown out, you can start fresh with a color that's closer to what you actually want, making future touch-ups much easier.
Your gray hair's resistance to color is actually quite common and has a straightforward solution. Gray hair has a different structure than pigmented hair. The cuticle is often more tightly closed, making it harder for color molecules to penetrate. You can find special additives designed specifically for gray coverage that help open the hair cuticle and allow better color penetration. These products will eliminate your need to use harsh black color just to get any color to stick.
For your thinning hair concern, be extra gentle during any color processing. Consider using lower-volume developers when possible, and always follow up with deep conditioning treatments. Some people find that slightly lighter colors can actually make thin hair appear fuller by creating more contrast with the scalp.
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See also:
Gray hair Q&A
How to color your own hair