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Simplifying 4(3x + 5) + -6(4x + -5) = 10x + 3(2x + -6) Reorder the terms: 4(5 + 3x) + -6(4x + -5) = 10x + 3(2x + -6) (5 * 4 + 3x * 4) + -6(4x + -5) = 10x + 3(2x + -6) (20 + 12x) + -6(4x + -5) = 10x + 3(2x + -6) Reorder the terms: 20 + 12x + -6(-5 + 4x) = 10x + 3(2x + -6) 20 + 12x + (-5 * -6 + 4x * -6) = 10x + 3(2x + -6) 20 + 12x + (30 + -24x) = 10x + 3(2x + -6) Reorder the terms: 20 + 30 + 12x + -24x = 10x + 3(2x + -6) Combine like terms: 20 + 30 = 50 50 + 12x + -24x = 10x + 3(2x + -6) Combine like terms: 12x + -24x = -12x 50 + -12x = 10x + 3(2x + -6) Reorder the terms: 50 + -12x = 10x + 3(-6 + 2x) 50 + -12x = 10x + (-6 * 3 + 2x * 3) 50 + -12x = 10x + (-18 + 6x) Reorder the terms: 50 + -12x = -18 + 10x + 6x Combine like terms: 10x + 6x = 16x 50 + -12x = -18 + 16x Solving 50 + -12x = -18 + 16x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16x' to each side of the equation. 50 + -12x + -16x = -18 + 16x + -16x Combine like terms: -12x + -16x = -28x 50 + -28x = -18 + 16x + -16x Combine like terms: 16x + -16x = 0 50 + -28x = -18 + 0 50 + -28x = -18 Add '-50' to each side of the equation. 50 + -50 + -28x = -18 + -50 Combine like terms: 50 + -50 = 0 0 + -28x = -18 + -50 -28x = -18 + -50 Combine like terms: -18 + -50 = -68 -28x = -68 Divide each side by '-28'. x = 2.428571429 Simplifying x = 2.428571429
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