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Simplifying 3y + -8 + 2x + -8(y + -1x + 3) + -5x + -2(x + -10) = 2x + -4(y + -1x) + 3(2x + -1y + 3) Reorder the terms: 3y + -8 + 2x + -8(3 + -1x + y) + -5x + -2(x + -10) = 2x + -4(y + -1x) + 3(2x + -1y + 3) 3y + -8 + 2x + (3 * -8 + -1x * -8 + y * -8) + -5x + -2(x + -10) = 2x + -4(y + -1x) + 3(2x + -1y + 3) 3y + -8 + 2x + (-24 + 8x + -8y) + -5x + -2(x + -10) = 2x + -4(y + -1x) + 3(2x + -1y + 3) Reorder the terms: 3y + -8 + 2x + -24 + 8x + -8y + -5x + -2(-10 + x) = 2x + -4(y + -1x) + 3(2x + -1y + 3) 3y + -8 + 2x + -24 + 8x + -8y + -5x + (-10 * -2 + x * -2) = 2x + -4(y + -1x) + 3(2x + -1y + 3) 3y + -8 + 2x + -24 + 8x + -8y + -5x + (20 + -2x) = 2x + -4(y + -1x) + 3(2x + -1y + 3) Reorder the terms: -8 + -24 + 20 + 2x + 8x + -5x + -2x + 3y + -8y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Combine like terms: -8 + -24 = -32 -32 + 20 + 2x + 8x + -5x + -2x + 3y + -8y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Combine like terms: -32 + 20 = -12 -12 + 2x + 8x + -5x + -2x + 3y + -8y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Combine like terms: 2x + 8x = 10x -12 + 10x + -5x + -2x + 3y + -8y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Combine like terms: 10x + -5x = 5x -12 + 5x + -2x + 3y + -8y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Combine like terms: 5x + -2x = 3x -12 + 3x + 3y + -8y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Combine like terms: 3y + -8y = -5y -12 + 3x + -5y = 2x + -4(y + -1x) + 3(2x + -1y + 3) Reorder the terms: -12 + 3x + -5y = 2x + -4(-1x + y) + 3(2x + -1y + 3) -12 + 3x + -5y = 2x + (-1x * -4 + y * -4) + 3(2x + -1y + 3) -12 + 3x + -5y = 2x + (4x + -4y) + 3(2x + -1y + 3) Reorder the terms: -12 + 3x + -5y = 2x + 4x + -4y + 3(3 + 2x + -1y) -12 + 3x + -5y = 2x + 4x + -4y + (3 * 3 + 2x * 3 + -1y * 3) -12 + 3x + -5y = 2x + 4x + -4y + (9 + 6x + -3y) Reorder the terms: -12 + 3x + -5y = 9 + 2x + 4x + 6x + -4y + -3y Combine like terms: 2x + 4x = 6x -12 + 3x + -5y = 9 + 6x + 6x + -4y + -3y Combine like terms: 6x + 6x = 12x -12 + 3x + -5y = 9 + 12x + -4y + -3y Combine like terms: -4y + -3y = -7y -12 + 3x + -5y = 9 + 12x + -7y Solving -12 + 3x + -5y = 9 + 12x + -7y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. -12 + 3x + -12x + -5y = 9 + 12x + -12x + -7y Combine like terms: 3x + -12x = -9x -12 + -9x + -5y = 9 + 12x + -12x + -7y Combine like terms: 12x + -12x = 0 -12 + -9x + -5y = 9 + 0 + -7y -12 + -9x + -5y = 9 + -7y Add '12' to each side of the equation. -12 + -9x + 12 + -5y = 9 + 12 + -7y Reorder the terms: -12 + 12 + -9x + -5y = 9 + 12 + -7y Combine like terms: -12 + 12 = 0 0 + -9x + -5y = 9 + 12 + -7y -9x + -5y = 9 + 12 + -7y Combine like terms: 9 + 12 = 21 -9x + -5y = 21 + -7y Add '5y' to each side of the equation. -9x + -5y + 5y = 21 + -7y + 5y Combine like terms: -5y + 5y = 0 -9x + 0 = 21 + -7y + 5y -9x = 21 + -7y + 5y Combine like terms: -7y + 5y = -2y -9x = 21 + -2y Divide each side by '-9'. x = -2.333333333 + 0.2222222222y Simplifying x = -2.333333333 + 0.2222222222y
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