(a-1)x+(b-1)x=(x-1)a+(x-1)b

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Solution for (a-1)x+(b-1)x=(x-1)a+(x-1)b equation: 


Simplifying
(a + -1) * x + (b + -1) * x = (x + -1) * a + (x + -1) * b

Reorder the terms:
(-1 + a) * x + (b + -1) * x = (x + -1) * a + (x + -1) * b

Reorder the terms for easier multiplication:
x(-1 + a) + (b + -1) * x = (x + -1) * a + (x + -1) * b
(-1 * x + a * x) + (b + -1) * x = (x + -1) * a + (x + -1) * b

Reorder the terms:
(ax + -1x) + (b + -1) * x = (x + -1) * a + (x + -1) * b
(ax + -1x) + (b + -1) * x = (x + -1) * a + (x + -1) * b

Reorder the terms:
ax + -1x + (-1 + b) * x = (x + -1) * a + (x + -1) * b

Reorder the terms for easier multiplication:
ax + -1x + x(-1 + b) = (x + -1) * a + (x + -1) * b
ax + -1x + (-1 * x + b * x) = (x + -1) * a + (x + -1) * b

Reorder the terms:
ax + -1x + (bx + -1x) = (x + -1) * a + (x + -1) * b
ax + -1x + (bx + -1x) = (x + -1) * a + (x + -1) * b

Reorder the terms:
ax + bx + -1x + -1x = (x + -1) * a + (x + -1) * b

Combine like terms: -1x + -1x = -2x
ax + bx + -2x = (x + -1) * a + (x + -1) * b

Reorder the terms:
ax + bx + -2x = (-1 + x) * a + (x + -1) * b

Reorder the terms for easier multiplication:
ax + bx + -2x = a(-1 + x) + (x + -1) * b
ax + bx + -2x = (-1 * a + x * a) + (x + -1) * b
ax + bx + -2x = (-1a + ax) + (x + -1) * b

Reorder the terms:
ax + bx + -2x = -1a + ax + (-1 + x) * b

Reorder the terms for easier multiplication:
ax + bx + -2x = -1a + ax + b(-1 + x)
ax + bx + -2x = -1a + ax + (-1 * b + x * b)
ax + bx + -2x = -1a + ax + (-1b + bx)

Add '-1ax' to each side of the equation.
ax + bx + -1ax + -2x = -1a + ax + -1b + -1ax + bx

Reorder the terms:
ax + -1ax + bx + -2x = -1a + ax + -1b + -1ax + bx

Combine like terms: ax + -1ax = 0
0 + bx + -2x = -1a + ax + -1b + -1ax + bx
bx + -2x = -1a + ax + -1b + -1ax + bx

Reorder the terms:
bx + -2x = -1a + ax + -1ax + -1b + bx

Combine like terms: ax + -1ax = 0
bx + -2x = -1a + 0 + -1b + bx
bx + -2x = -1a + -1b + bx

Add '-1bx' to each side of the equation.
bx + -1bx + -2x = -1a + -1b + bx + -1bx

Combine like terms: bx + -1bx = 0
0 + -2x = -1a + -1b + bx + -1bx
-2x = -1a + -1b + bx + -1bx

Combine like terms: bx + -1bx = 0
-2x = -1a + -1b + 0
-2x = -1a + -1b

Solving
-2x = -1a + -1b

Solving for variable 'x'.

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

Divide each side by '-2'.
x = 0.5a + 0.5b

Simplifying
x = 0.5a + 0.5b

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