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Simplifying 3(x + -5) + 2(x + 3) = 2(4x + -5) + 4(x + 7) Reorder the terms: 3(-5 + x) + 2(x + 3) = 2(4x + -5) + 4(x + 7) (-5 * 3 + x * 3) + 2(x + 3) = 2(4x + -5) + 4(x + 7) (-15 + 3x) + 2(x + 3) = 2(4x + -5) + 4(x + 7) Reorder the terms: -15 + 3x + 2(3 + x) = 2(4x + -5) + 4(x + 7) -15 + 3x + (3 * 2 + x * 2) = 2(4x + -5) + 4(x + 7) -15 + 3x + (6 + 2x) = 2(4x + -5) + 4(x + 7) Reorder the terms: -15 + 6 + 3x + 2x = 2(4x + -5) + 4(x + 7) Combine like terms: -15 + 6 = -9 -9 + 3x + 2x = 2(4x + -5) + 4(x + 7) Combine like terms: 3x + 2x = 5x -9 + 5x = 2(4x + -5) + 4(x + 7) Reorder the terms: -9 + 5x = 2(-5 + 4x) + 4(x + 7) -9 + 5x = (-5 * 2 + 4x * 2) + 4(x + 7) -9 + 5x = (-10 + 8x) + 4(x + 7) Reorder the terms: -9 + 5x = -10 + 8x + 4(7 + x) -9 + 5x = -10 + 8x + (7 * 4 + x * 4) -9 + 5x = -10 + 8x + (28 + 4x) Reorder the terms: -9 + 5x = -10 + 28 + 8x + 4x Combine like terms: -10 + 28 = 18 -9 + 5x = 18 + 8x + 4x Combine like terms: 8x + 4x = 12x -9 + 5x = 18 + 12x Solving -9 + 5x = 18 + 12x 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. -9 + 5x + -12x = 18 + 12x + -12x Combine like terms: 5x + -12x = -7x -9 + -7x = 18 + 12x + -12x Combine like terms: 12x + -12x = 0 -9 + -7x = 18 + 0 -9 + -7x = 18 Add '9' to each side of the equation. -9 + 9 + -7x = 18 + 9 Combine like terms: -9 + 9 = 0 0 + -7x = 18 + 9 -7x = 18 + 9 Combine like terms: 18 + 9 = 27 -7x = 27 Divide each side by '-7'. x = -3.857142857 Simplifying x = -3.857142857
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