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Simplifying 3(2x + 1) = 4(2x + 5) + -2(2x + 3) + 19 Reorder the terms: 3(1 + 2x) = 4(2x + 5) + -2(2x + 3) + 19 (1 * 3 + 2x * 3) = 4(2x + 5) + -2(2x + 3) + 19 (3 + 6x) = 4(2x + 5) + -2(2x + 3) + 19 Reorder the terms: 3 + 6x = 4(5 + 2x) + -2(2x + 3) + 19 3 + 6x = (5 * 4 + 2x * 4) + -2(2x + 3) + 19 3 + 6x = (20 + 8x) + -2(2x + 3) + 19 Reorder the terms: 3 + 6x = 20 + 8x + -2(3 + 2x) + 19 3 + 6x = 20 + 8x + (3 * -2 + 2x * -2) + 19 3 + 6x = 20 + 8x + (-6 + -4x) + 19 Reorder the terms: 3 + 6x = 20 + -6 + 19 + 8x + -4x Combine like terms: 20 + -6 = 14 3 + 6x = 14 + 19 + 8x + -4x Combine like terms: 14 + 19 = 33 3 + 6x = 33 + 8x + -4x Combine like terms: 8x + -4x = 4x 3 + 6x = 33 + 4x Solving 3 + 6x = 33 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 3 + 6x + -4x = 33 + 4x + -4x Combine like terms: 6x + -4x = 2x 3 + 2x = 33 + 4x + -4x Combine like terms: 4x + -4x = 0 3 + 2x = 33 + 0 3 + 2x = 33 Add '-3' to each side of the equation. 3 + -3 + 2x = 33 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 33 + -3 2x = 33 + -3 Combine like terms: 33 + -3 = 30 2x = 30 Divide each side by '2'. x = 15 Simplifying x = 15
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