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Simplifying 3(x + -6) + 12(2x + 5) = 10(2x + 7) Reorder the terms: 3(-6 + x) + 12(2x + 5) = 10(2x + 7) (-6 * 3 + x * 3) + 12(2x + 5) = 10(2x + 7) (-18 + 3x) + 12(2x + 5) = 10(2x + 7) Reorder the terms: -18 + 3x + 12(5 + 2x) = 10(2x + 7) -18 + 3x + (5 * 12 + 2x * 12) = 10(2x + 7) -18 + 3x + (60 + 24x) = 10(2x + 7) Reorder the terms: -18 + 60 + 3x + 24x = 10(2x + 7) Combine like terms: -18 + 60 = 42 42 + 3x + 24x = 10(2x + 7) Combine like terms: 3x + 24x = 27x 42 + 27x = 10(2x + 7) Reorder the terms: 42 + 27x = 10(7 + 2x) 42 + 27x = (7 * 10 + 2x * 10) 42 + 27x = (70 + 20x) Solving 42 + 27x = 70 + 20x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20x' to each side of the equation. 42 + 27x + -20x = 70 + 20x + -20x Combine like terms: 27x + -20x = 7x 42 + 7x = 70 + 20x + -20x Combine like terms: 20x + -20x = 0 42 + 7x = 70 + 0 42 + 7x = 70 Add '-42' to each side of the equation. 42 + -42 + 7x = 70 + -42 Combine like terms: 42 + -42 = 0 0 + 7x = 70 + -42 7x = 70 + -42 Combine like terms: 70 + -42 = 28 7x = 28 Divide each side by '7'. x = 4 Simplifying x = 4
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