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Simplifying 0.5(3x + 5) + -0.1(12x + -5) = 3(1 + 0.1) Reorder the terms: 0.5(5 + 3x) + -0.1(12x + -5) = 3(1 + 0.1) (5 * 0.5 + 3x * 0.5) + -0.1(12x + -5) = 3(1 + 0.1) (2.5 + 1.5x) + -0.1(12x + -5) = 3(1 + 0.1) Reorder the terms: 2.5 + 1.5x + -0.1(-5 + 12x) = 3(1 + 0.1) 2.5 + 1.5x + (-5 * -0.1 + 12x * -0.1) = 3(1 + 0.1) 2.5 + 1.5x + (0.5 + -1.2x) = 3(1 + 0.1) Reorder the terms: 2.5 + 0.5 + 1.5x + -1.2x = 3(1 + 0.1) Combine like terms: 2.5 + 0.5 = 3 3 + 1.5x + -1.2x = 3(1 + 0.1) Combine like terms: 1.5x + -1.2x = 0.3x 3 + 0.3x = 3(1 + 0.1) Combine like terms: 1 + 0.1 = 1.1 3 + 0.3x = 3(1.1) Multiply 3 * 1.1 3 + 0.3x = 3.3 Solving 3 + 0.3x = 3.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 0.3x = 3.3 + -3 Combine like terms: 3 + -3 = 0 0 + 0.3x = 3.3 + -3 0.3x = 3.3 + -3 Combine like terms: 3.3 + -3 = 0.3 0.3x = 0.3 Divide each side by '0.3'. x = 1 Simplifying x = 1
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