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

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


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

Reorder the terms:
(-2 + y) + -1(y + 1) = (y + -3) + -2

Remove parenthesis around (-2 + y)
-2 + y + -1(y + 1) = (y + -3) + -2

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

Reorder the terms:
-2 + -1 + y + -1y = (y + -3) + -2

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

Combine like terms: y + -1y = 0
-3 + 0 = (y + -3) + -2
-3 = (y + -3) + -2

Reorder the terms:
-3 = (-3 + y) + -2

Remove parenthesis around (-3 + y)
-3 = -3 + y + -2

Reorder the terms:
-3 = -3 + -2 + y

Combine like terms: -3 + -2 = -5
-3 = -5 + y

Solving
-3 = -5 + y

Solving for variable 'y'.

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

Add '-1y' to each side of the equation.
-3 + -1y = -5 + y + -1y

Combine like terms: y + -1y = 0
-3 + -1y = -5 + 0
-3 + -1y = -5

Add '3' to each side of the equation.
-3 + 3 + -1y = -5 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = -5 + 3
-1y = -5 + 3

Combine like terms: -5 + 3 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2

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