2(x-3)+(x-1)=2(x-1)

Solution for 2(x-3)+(x-1)=2(x-1) equation:

Simplifying
2(x + -3) + (x + -1) = 2(x + -1)

Reorder the terms:
2(-3 + x) + (x + -1) = 2(x + -1)
(-3 * 2 + x * 2) + (x + -1) = 2(x + -1)
(-6 + 2x) + (x + -1) = 2(x + -1)

Reorder the terms:
-6 + 2x + (-1 + x) = 2(x + -1)

Remove parenthesis around (-1 + x)
-6 + 2x + -1 + x = 2(x + -1)

Reorder the terms:
-6 + -1 + 2x + x = 2(x + -1)

Combine like terms: -6 + -1 = -7
-7 + 2x + x = 2(x + -1)

Combine like terms: 2x + x = 3x
-7 + 3x = 2(x + -1)

Reorder the terms:
-7 + 3x = 2(-1 + x)
-7 + 3x = (-1 * 2 + x * 2)
-7 + 3x = (-2 + 2x)

Solving
-7 + 3x = -2 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-7 + 3x + -2x = -2 + 2x + -2x

Combine like terms: 3x + -2x = 1x
-7 + 1x = -2 + 2x + -2x

Combine like terms: 2x + -2x = 0
-7 + 1x = -2 + 0
-7 + 1x = -2

Add '7' to each side of the equation.
-7 + 7 + 1x = -2 + 7

Combine like terms: -7 + 7 = 0
0 + 1x = -2 + 7
1x = -2 + 7

Combine like terms: -2 + 7 = 5
1x = 5

Divide each side by '1'.
x = 5

Simplifying
x = 5