x-(x-1)-(x-3)=10

Solution for x-(x-1)-(x-3)=10 equation:

Simplifying
x + -1(x + -1) + -1(x + -3) = 10

Reorder the terms:
x + -1(-1 + x) + -1(x + -3) = 10
x + (-1 * -1 + x * -1) + -1(x + -3) = 10
x + (1 + -1x) + -1(x + -3) = 10

Reorder the terms:
x + 1 + -1x + -1(-3 + x) = 10
x + 1 + -1x + (-3 * -1 + x * -1) = 10
x + 1 + -1x + (3 + -1x) = 10

Reorder the terms:
1 + 3 + x + -1x + -1x = 10

Combine like terms: 1 + 3 = 4
4 + x + -1x + -1x = 10

Combine like terms: x + -1x = 0
4 + 0 + -1x = 10
4 + -1x = 10

Solving
4 + -1x = 10

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 10 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 10 + -4
-1x = 10 + -4

Combine like terms: 10 + -4 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6