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Simplifying 2(4x + -5) + 11(6x + 2) = 3(x + 1) + -5(2x + 3) Reorder the terms: 2(-5 + 4x) + 11(6x + 2) = 3(x + 1) + -5(2x + 3) (-5 * 2 + 4x * 2) + 11(6x + 2) = 3(x + 1) + -5(2x + 3) (-10 + 8x) + 11(6x + 2) = 3(x + 1) + -5(2x + 3) Reorder the terms: -10 + 8x + 11(2 + 6x) = 3(x + 1) + -5(2x + 3) -10 + 8x + (2 * 11 + 6x * 11) = 3(x + 1) + -5(2x + 3) -10 + 8x + (22 + 66x) = 3(x + 1) + -5(2x + 3) Reorder the terms: -10 + 22 + 8x + 66x = 3(x + 1) + -5(2x + 3) Combine like terms: -10 + 22 = 12 12 + 8x + 66x = 3(x + 1) + -5(2x + 3) Combine like terms: 8x + 66x = 74x 12 + 74x = 3(x + 1) + -5(2x + 3) Reorder the terms: 12 + 74x = 3(1 + x) + -5(2x + 3) 12 + 74x = (1 * 3 + x * 3) + -5(2x + 3) 12 + 74x = (3 + 3x) + -5(2x + 3) Reorder the terms: 12 + 74x = 3 + 3x + -5(3 + 2x) 12 + 74x = 3 + 3x + (3 * -5 + 2x * -5) 12 + 74x = 3 + 3x + (-15 + -10x) Reorder the terms: 12 + 74x = 3 + -15 + 3x + -10x Combine like terms: 3 + -15 = -12 12 + 74x = -12 + 3x + -10x Combine like terms: 3x + -10x = -7x 12 + 74x = -12 + -7x Solving 12 + 74x = -12 + -7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7x' to each side of the equation. 12 + 74x + 7x = -12 + -7x + 7x Combine like terms: 74x + 7x = 81x 12 + 81x = -12 + -7x + 7x Combine like terms: -7x + 7x = 0 12 + 81x = -12 + 0 12 + 81x = -12 Add '-12' to each side of the equation. 12 + -12 + 81x = -12 + -12 Combine like terms: 12 + -12 = 0 0 + 81x = -12 + -12 81x = -12 + -12 Combine like terms: -12 + -12 = -24 81x = -24 Divide each side by '81'. x = -0.2962962963 Simplifying x = -0.2962962963
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