22-[5+6y-3(y+2)]=-4(4y-3)-[7(y-1)-16y+8]

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Solution for 22-[5+6y-3(y+2)]=-4(4y-3)-[7(y-1)-16y+8] equation:


Simplifying
22 + -1[5 + 6y + -3(y + 2)] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]

Reorder the terms:
22 + -1[5 + 6y + -3(2 + y)] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]
22 + -1[5 + 6y + (2 * -3 + y * -3)] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]
22 + -1[5 + 6y + (-6 + -3y)] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]

Reorder the terms:
22 + -1[5 + -6 + 6y + -3y] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]

Combine like terms: 5 + -6 = -1
22 + -1[-1 + 6y + -3y] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]

Combine like terms: 6y + -3y = 3y
22 + -1[-1 + 3y] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]
22 + [-1 * -1 + 3y * -1] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]
22 + [1 + -3y] = -4(4y + -3) + -1[7(y + -1) + -16y + 8]

Combine like terms: 22 + 1 = 23
23 + -3y = -4(4y + -3) + -1[7(y + -1) + -16y + 8]

Reorder the terms:
23 + -3y = -4(-3 + 4y) + -1[7(y + -1) + -16y + 8]
23 + -3y = (-3 * -4 + 4y * -4) + -1[7(y + -1) + -16y + 8]
23 + -3y = (12 + -16y) + -1[7(y + -1) + -16y + 8]

Reorder the terms:
23 + -3y = 12 + -16y + -1[7(-1 + y) + -16y + 8]
23 + -3y = 12 + -16y + -1[(-1 * 7 + y * 7) + -16y + 8]
23 + -3y = 12 + -16y + -1[(-7 + 7y) + -16y + 8]

Reorder the terms:
23 + -3y = 12 + -16y + -1[-7 + 8 + 7y + -16y]

Combine like terms: -7 + 8 = 1
23 + -3y = 12 + -16y + -1[1 + 7y + -16y]

Combine like terms: 7y + -16y = -9y
23 + -3y = 12 + -16y + -1[1 + -9y]
23 + -3y = 12 + -16y + [1 * -1 + -9y * -1]
23 + -3y = 12 + -16y + [-1 + 9y]

Reorder the terms:
23 + -3y = 12 + -1 + -16y + 9y

Combine like terms: 12 + -1 = 11
23 + -3y = 11 + -16y + 9y

Combine like terms: -16y + 9y = -7y
23 + -3y = 11 + -7y

Solving
23 + -3y = 11 + -7y

Solving for variable 'y'.

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

Add '7y' to each side of the equation.
23 + -3y + 7y = 11 + -7y + 7y

Combine like terms: -3y + 7y = 4y
23 + 4y = 11 + -7y + 7y

Combine like terms: -7y + 7y = 0
23 + 4y = 11 + 0
23 + 4y = 11

Add '-23' to each side of the equation.
23 + -23 + 4y = 11 + -23

Combine like terms: 23 + -23 = 0
0 + 4y = 11 + -23
4y = 11 + -23

Combine like terms: 11 + -23 = -12
4y = -12

Divide each side by '4'.
y = -3

Simplifying
y = -3

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