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Simplifying 12(4x + 9y + 2) + 10(8x + 7y + 4) = 120 Reorder the terms: 12(2 + 4x + 9y) + 10(8x + 7y + 4) = 120 (2 * 12 + 4x * 12 + 9y * 12) + 10(8x + 7y + 4) = 120 (24 + 48x + 108y) + 10(8x + 7y + 4) = 120 Reorder the terms: 24 + 48x + 108y + 10(4 + 8x + 7y) = 120 24 + 48x + 108y + (4 * 10 + 8x * 10 + 7y * 10) = 120 24 + 48x + 108y + (40 + 80x + 70y) = 120 Reorder the terms: 24 + 40 + 48x + 80x + 108y + 70y = 120 Combine like terms: 24 + 40 = 64 64 + 48x + 80x + 108y + 70y = 120 Combine like terms: 48x + 80x = 128x 64 + 128x + 108y + 70y = 120 Combine like terms: 108y + 70y = 178y 64 + 128x + 178y = 120 Solving 64 + 128x + 178y = 120 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + 128x + -64 + 178y = 120 + -64 Reorder the terms: 64 + -64 + 128x + 178y = 120 + -64 Combine like terms: 64 + -64 = 0 0 + 128x + 178y = 120 + -64 128x + 178y = 120 + -64 Combine like terms: 120 + -64 = 56 128x + 178y = 56 Add '-178y' to each side of the equation. 128x + 178y + -178y = 56 + -178y Combine like terms: 178y + -178y = 0 128x + 0 = 56 + -178y 128x = 56 + -178y Divide each side by '128'. x = 0.4375 + -1.390625y Simplifying x = 0.4375 + -1.390625y
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