When x Is Negative

In $10-x = 2x+1$, the x on the left has coefficient $-1$. To collect toward the larger coefficient, move it to the right: add x to both sides.

$$10 = 3x+1$$

$$9 = 3x$$

$$3 = x$$

Swap the sides to write it in the usual form, $x = 3$. Check: $10-3 = 7$ and $2\cdot 3+1 = 7$.

Adding an x-term to both sides is allowed in the same way as subtracting one. It is the step to use whenever an x-term has a minus sign in front of it. You could instead subtract $2x$ from both sides and get $10-3x = 1$. That also works, but the coefficient stays negative until the end.