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Simplifying 1.4(0.2x + 1.3) = 0.5(0.1x + 4.56) Reorder the terms: 1.4(1.3 + 0.2x) = 0.5(0.1x + 4.56) (1.3 * 1.4 + 0.2x * 1.4) = 0.5(0.1x + 4.56) (1.82 + 0.28x) = 0.5(0.1x + 4.56) Reorder the terms: 1.82 + 0.28x = 0.5(4.56 + 0.1x) 1.82 + 0.28x = (4.56 * 0.5 + 0.1x * 0.5) 1.82 + 0.28x = (2.28 + 0.05x) Solving 1.82 + 0.28x = 2.28 + 0.05x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05x' to each side of the equation. 1.82 + 0.28x + -0.05x = 2.28 + 0.05x + -0.05x Combine like terms: 0.28x + -0.05x = 0.23x 1.82 + 0.23x = 2.28 + 0.05x + -0.05x Combine like terms: 0.05x + -0.05x = 0.00 1.82 + 0.23x = 2.28 + 0.00 1.82 + 0.23x = 2.28 Add '-1.82' to each side of the equation. 1.82 + -1.82 + 0.23x = 2.28 + -1.82 Combine like terms: 1.82 + -1.82 = 0.00 0.00 + 0.23x = 2.28 + -1.82 0.23x = 2.28 + -1.82 Combine like terms: 2.28 + -1.82 = 0.46 0.23x = 0.46 Divide each side by '0.23'. x = 2 Simplifying x = 2
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