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Simplifying 5(2x + 3) = 3(4x + 1) + -2(3x + 2) Reorder the terms: 5(3 + 2x) = 3(4x + 1) + -2(3x + 2) (3 * 5 + 2x * 5) = 3(4x + 1) + -2(3x + 2) (15 + 10x) = 3(4x + 1) + -2(3x + 2) Reorder the terms: 15 + 10x = 3(1 + 4x) + -2(3x + 2) 15 + 10x = (1 * 3 + 4x * 3) + -2(3x + 2) 15 + 10x = (3 + 12x) + -2(3x + 2) Reorder the terms: 15 + 10x = 3 + 12x + -2(2 + 3x) 15 + 10x = 3 + 12x + (2 * -2 + 3x * -2) 15 + 10x = 3 + 12x + (-4 + -6x) Reorder the terms: 15 + 10x = 3 + -4 + 12x + -6x Combine like terms: 3 + -4 = -1 15 + 10x = -1 + 12x + -6x Combine like terms: 12x + -6x = 6x 15 + 10x = -1 + 6x Solving 15 + 10x = -1 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 15 + 10x + -6x = -1 + 6x + -6x Combine like terms: 10x + -6x = 4x 15 + 4x = -1 + 6x + -6x Combine like terms: 6x + -6x = 0 15 + 4x = -1 + 0 15 + 4x = -1 Add '-15' to each side of the equation. 15 + -15 + 4x = -1 + -15 Combine like terms: 15 + -15 = 0 0 + 4x = -1 + -15 4x = -1 + -15 Combine like terms: -1 + -15 = -16 4x = -16 Divide each side by '4'. x = -4 Simplifying x = -4
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