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Simplifying 6(2x + 2) + 2(3x + -6) = 10(x + 15) + 2(x + 5) Reorder the terms: 6(2 + 2x) + 2(3x + -6) = 10(x + 15) + 2(x + 5) (2 * 6 + 2x * 6) + 2(3x + -6) = 10(x + 15) + 2(x + 5) (12 + 12x) + 2(3x + -6) = 10(x + 15) + 2(x + 5) Reorder the terms: 12 + 12x + 2(-6 + 3x) = 10(x + 15) + 2(x + 5) 12 + 12x + (-6 * 2 + 3x * 2) = 10(x + 15) + 2(x + 5) 12 + 12x + (-12 + 6x) = 10(x + 15) + 2(x + 5) Reorder the terms: 12 + -12 + 12x + 6x = 10(x + 15) + 2(x + 5) Combine like terms: 12 + -12 = 0 0 + 12x + 6x = 10(x + 15) + 2(x + 5) 12x + 6x = 10(x + 15) + 2(x + 5) Combine like terms: 12x + 6x = 18x 18x = 10(x + 15) + 2(x + 5) Reorder the terms: 18x = 10(15 + x) + 2(x + 5) 18x = (15 * 10 + x * 10) + 2(x + 5) 18x = (150 + 10x) + 2(x + 5) Reorder the terms: 18x = 150 + 10x + 2(5 + x) 18x = 150 + 10x + (5 * 2 + x * 2) 18x = 150 + 10x + (10 + 2x) Reorder the terms: 18x = 150 + 10 + 10x + 2x Combine like terms: 150 + 10 = 160 18x = 160 + 10x + 2x Combine like terms: 10x + 2x = 12x 18x = 160 + 12x Solving 18x = 160 + 12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. 18x + -12x = 160 + 12x + -12x Combine like terms: 18x + -12x = 6x 6x = 160 + 12x + -12x Combine like terms: 12x + -12x = 0 6x = 160 + 0 6x = 160 Divide each side by '6'. x = 26.66666667 Simplifying x = 26.66666667
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