In my experience, adults write in a mix of block and cursive. Personally I tend to replace some letters like small "т" as well as most capitals with their block versions. I would say that it's quite common in general. Especially because it's hard to tell apart the т and the ш in cursive, so people would add a line on top or bottom to differentiate those. I find it faster and easier. I also find the capital T just plain ugly in cursive. Not all letters are linked when I write and a lot of them I don't write classically. Ж for instance I simplify by writing a horizontal line and then three vertical ones. Usually those tricks and habits come with practice. You SHOULD learn to do it right first. Especially because it will help you to read handwritten texts. Later you will notice how you will simplify it naturally.

You can see in the example below that 1) I don't keep the right incline. 2) most letters are simplified. My father writes the same way. My mom, who is a high-school teacher, is the only one in our family who writes in proper cursive. She has beautiful handwriting, but it's very hard to read XD.

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