23-[1+4y-2(y+5)]=-4(3y-7)-[7(y-1)-10y+24]

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Solution for 23-[1+4y-2(y+5)]=-4(3y-7)-[7(y-1)-10y+24] equation:


Simplifying
23 + -1[1 + 4y + -2(y + 5)] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]

Reorder the terms:
23 + -1[1 + 4y + -2(5 + y)] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]
23 + -1[1 + 4y + (5 * -2 + y * -2)] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]
23 + -1[1 + 4y + (-10 + -2y)] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]

Reorder the terms:
23 + -1[1 + -10 + 4y + -2y] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]

Combine like terms: 1 + -10 = -9
23 + -1[-9 + 4y + -2y] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]

Combine like terms: 4y + -2y = 2y
23 + -1[-9 + 2y] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]
23 + [-9 * -1 + 2y * -1] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]
23 + [9 + -2y] = -4(3y + -7) + -1[7(y + -1) + -10y + 24]

Combine like terms: 23 + 9 = 32
32 + -2y = -4(3y + -7) + -1[7(y + -1) + -10y + 24]

Reorder the terms:
32 + -2y = -4(-7 + 3y) + -1[7(y + -1) + -10y + 24]
32 + -2y = (-7 * -4 + 3y * -4) + -1[7(y + -1) + -10y + 24]
32 + -2y = (28 + -12y) + -1[7(y + -1) + -10y + 24]

Reorder the terms:
32 + -2y = 28 + -12y + -1[7(-1 + y) + -10y + 24]
32 + -2y = 28 + -12y + -1[(-1 * 7 + y * 7) + -10y + 24]
32 + -2y = 28 + -12y + -1[(-7 + 7y) + -10y + 24]

Reorder the terms:
32 + -2y = 28 + -12y + -1[-7 + 24 + 7y + -10y]

Combine like terms: -7 + 24 = 17
32 + -2y = 28 + -12y + -1[17 + 7y + -10y]

Combine like terms: 7y + -10y = -3y
32 + -2y = 28 + -12y + -1[17 + -3y]
32 + -2y = 28 + -12y + [17 * -1 + -3y * -1]
32 + -2y = 28 + -12y + [-17 + 3y]

Reorder the terms:
32 + -2y = 28 + -17 + -12y + 3y

Combine like terms: 28 + -17 = 11
32 + -2y = 11 + -12y + 3y

Combine like terms: -12y + 3y = -9y
32 + -2y = 11 + -9y

Solving
32 + -2y = 11 + -9y

Solving for variable 'y'.

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

Add '9y' to each side of the equation.
32 + -2y + 9y = 11 + -9y + 9y

Combine like terms: -2y + 9y = 7y
32 + 7y = 11 + -9y + 9y

Combine like terms: -9y + 9y = 0
32 + 7y = 11 + 0
32 + 7y = 11

Add '-32' to each side of the equation.
32 + -32 + 7y = 11 + -32

Combine like terms: 32 + -32 = 0
0 + 7y = 11 + -32
7y = 11 + -32

Combine like terms: 11 + -32 = -21
7y = -21

Divide each side by '7'.
y = -3

Simplifying
y = -3

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