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Simplifying 4(3x + 5) + -6(4x + -5) = 12x + 3(2x + -8) Reorder the terms: 4(5 + 3x) + -6(4x + -5) = 12x + 3(2x + -8) (5 * 4 + 3x * 4) + -6(4x + -5) = 12x + 3(2x + -8) (20 + 12x) + -6(4x + -5) = 12x + 3(2x + -8) Reorder the terms: 20 + 12x + -6(-5 + 4x) = 12x + 3(2x + -8) 20 + 12x + (-5 * -6 + 4x * -6) = 12x + 3(2x + -8) 20 + 12x + (30 + -24x) = 12x + 3(2x + -8) Reorder the terms: 20 + 30 + 12x + -24x = 12x + 3(2x + -8) Combine like terms: 20 + 30 = 50 50 + 12x + -24x = 12x + 3(2x + -8) Combine like terms: 12x + -24x = -12x 50 + -12x = 12x + 3(2x + -8) Reorder the terms: 50 + -12x = 12x + 3(-8 + 2x) 50 + -12x = 12x + (-8 * 3 + 2x * 3) 50 + -12x = 12x + (-24 + 6x) Reorder the terms: 50 + -12x = -24 + 12x + 6x Combine like terms: 12x + 6x = 18x 50 + -12x = -24 + 18x Solving 50 + -12x = -24 + 18x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18x' to each side of the equation. 50 + -12x + -18x = -24 + 18x + -18x Combine like terms: -12x + -18x = -30x 50 + -30x = -24 + 18x + -18x Combine like terms: 18x + -18x = 0 50 + -30x = -24 + 0 50 + -30x = -24 Add '-50' to each side of the equation. 50 + -50 + -30x = -24 + -50 Combine like terms: 50 + -50 = 0 0 + -30x = -24 + -50 -30x = -24 + -50 Combine like terms: -24 + -50 = -74 -30x = -74 Divide each side by '-30'. x = 2.466666667 Simplifying x = 2.466666667
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