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Simplifying 0.5(3x + 5) + -0.1(12x + -5) = 3(1 + 0.1x) Reorder the terms: 0.5(5 + 3x) + -0.1(12x + -5) = 3(1 + 0.1x) (5 * 0.5 + 3x * 0.5) + -0.1(12x + -5) = 3(1 + 0.1x) (2.5 + 1.5x) + -0.1(12x + -5) = 3(1 + 0.1x) Reorder the terms: 2.5 + 1.5x + -0.1(-5 + 12x) = 3(1 + 0.1x) 2.5 + 1.5x + (-5 * -0.1 + 12x * -0.1) = 3(1 + 0.1x) 2.5 + 1.5x + (0.5 + -1.2x) = 3(1 + 0.1x) Reorder the terms: 2.5 + 0.5 + 1.5x + -1.2x = 3(1 + 0.1x) Combine like terms: 2.5 + 0.5 = 3 3 + 1.5x + -1.2x = 3(1 + 0.1x) Combine like terms: 1.5x + -1.2x = 0.3x 3 + 0.3x = 3(1 + 0.1x) 3 + 0.3x = (1 * 3 + 0.1x * 3) 3 + 0.3x = (3 + 0.3x) Add '-3' to each side of the equation. 3 + -3 + 0.3x = 3 + -3 + 0.3x Combine like terms: 3 + -3 = 0 0 + 0.3x = 3 + -3 + 0.3x 0.3x = 3 + -3 + 0.3x Combine like terms: 3 + -3 = 0 0.3x = 0 + 0.3x 0.3x = 0.3x Add '-0.3x' to each side of the equation. 0.3x + -0.3x = 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 0.0 = 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 0.0 = 0.0 Solving 0.0 = 0.0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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