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Simplifying 0.333(x + 3) + 9 = 0.5(9 + 3x) + 2 Reorder the terms: 0.333(3 + x) + 9 = 0.5(9 + 3x) + 2 (3 * 0.333 + x * 0.333) + 9 = 0.5(9 + 3x) + 2 (0.999 + 0.333x) + 9 = 0.5(9 + 3x) + 2 Reorder the terms: 0.999 + 9 + 0.333x = 0.5(9 + 3x) + 2 Combine like terms: 0.999 + 9 = 9.999 9.999 + 0.333x = 0.5(9 + 3x) + 2 9.999 + 0.333x = (9 * 0.5 + 3x * 0.5) + 2 9.999 + 0.333x = (4.5 + 1.5x) + 2 Reorder the terms: 9.999 + 0.333x = 4.5 + 2 + 1.5x Combine like terms: 4.5 + 2 = 6.5 9.999 + 0.333x = 6.5 + 1.5x Solving 9.999 + 0.333x = 6.5 + 1.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5x' to each side of the equation. 9.999 + 0.333x + -1.5x = 6.5 + 1.5x + -1.5x Combine like terms: 0.333x + -1.5x = -1.167x 9.999 + -1.167x = 6.5 + 1.5x + -1.5x Combine like terms: 1.5x + -1.5x = 0.0 9.999 + -1.167x = 6.5 + 0.0 9.999 + -1.167x = 6.5 Add '-9.999' to each side of the equation. 9.999 + -9.999 + -1.167x = 6.5 + -9.999 Combine like terms: 9.999 + -9.999 = 0.000 0.000 + -1.167x = 6.5 + -9.999 -1.167x = 6.5 + -9.999 Combine like terms: 6.5 + -9.999 = -3.499 -1.167x = -3.499 Divide each side by '-1.167'. x = 2.998286204 Simplifying x = 2.998286204
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