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Simplifying 12(8x + 7) + -45(4x + 5) = 4(16x + -31) + 15(1 + -4x) + -54 Reorder the terms: 12(7 + 8x) + -45(4x + 5) = 4(16x + -31) + 15(1 + -4x) + -54 (7 * 12 + 8x * 12) + -45(4x + 5) = 4(16x + -31) + 15(1 + -4x) + -54 (84 + 96x) + -45(4x + 5) = 4(16x + -31) + 15(1 + -4x) + -54 Reorder the terms: 84 + 96x + -45(5 + 4x) = 4(16x + -31) + 15(1 + -4x) + -54 84 + 96x + (5 * -45 + 4x * -45) = 4(16x + -31) + 15(1 + -4x) + -54 84 + 96x + (-225 + -180x) = 4(16x + -31) + 15(1 + -4x) + -54 Reorder the terms: 84 + -225 + 96x + -180x = 4(16x + -31) + 15(1 + -4x) + -54 Combine like terms: 84 + -225 = -141 -141 + 96x + -180x = 4(16x + -31) + 15(1 + -4x) + -54 Combine like terms: 96x + -180x = -84x -141 + -84x = 4(16x + -31) + 15(1 + -4x) + -54 Reorder the terms: -141 + -84x = 4(-31 + 16x) + 15(1 + -4x) + -54 -141 + -84x = (-31 * 4 + 16x * 4) + 15(1 + -4x) + -54 -141 + -84x = (-124 + 64x) + 15(1 + -4x) + -54 -141 + -84x = -124 + 64x + (1 * 15 + -4x * 15) + -54 -141 + -84x = -124 + 64x + (15 + -60x) + -54 Reorder the terms: -141 + -84x = -124 + 15 + -54 + 64x + -60x Combine like terms: -124 + 15 = -109 -141 + -84x = -109 + -54 + 64x + -60x Combine like terms: -109 + -54 = -163 -141 + -84x = -163 + 64x + -60x Combine like terms: 64x + -60x = 4x -141 + -84x = -163 + 4x Solving -141 + -84x = -163 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. -141 + -84x + -4x = -163 + 4x + -4x Combine like terms: -84x + -4x = -88x -141 + -88x = -163 + 4x + -4x Combine like terms: 4x + -4x = 0 -141 + -88x = -163 + 0 -141 + -88x = -163 Add '141' to each side of the equation. -141 + 141 + -88x = -163 + 141 Combine like terms: -141 + 141 = 0 0 + -88x = -163 + 141 -88x = -163 + 141 Combine like terms: -163 + 141 = -22 -88x = -22 Divide each side by '-88'. x = 0.25 Simplifying x = 0.25
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