False Position

You adopt a position

Let's say you are solving this classic Egyptian problem:

𝚡 + 𝚡/𝟽 = 𝟷𝟿

You can take a guess that makes check the left side easy

𝚡1 := 7 𝚡1 + 𝚡1/𝟽 = 8

If you fail, improve your guess