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Simplifying -51.442 = -2.3(3.1r + 0.9) + 3.5(0.3 + 2.2r) Reorder the terms: -51.442 = -2.3(0.9 + 3.1r) + 3.5(0.3 + 2.2r) -51.442 = (0.9 * -2.3 + 3.1r * -2.3) + 3.5(0.3 + 2.2r) -51.442 = (-2.07 + -7.13r) + 3.5(0.3 + 2.2r) -51.442 = -2.07 + -7.13r + (0.3 * 3.5 + 2.2r * 3.5) -51.442 = -2.07 + -7.13r + (1.05 + 7.7r) Reorder the terms: -51.442 = -2.07 + 1.05 + -7.13r + 7.7r Combine like terms: -2.07 + 1.05 = -1.02 -51.442 = -1.02 + -7.13r + 7.7r Combine like terms: -7.13r + 7.7r = 0.57r -51.442 = -1.02 + 0.57r Solving -51.442 = -1.02 + 0.57r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.57r' to each side of the equation. -51.442 + -0.57r = -1.02 + 0.57r + -0.57r Combine like terms: 0.57r + -0.57r = 0.00 -51.442 + -0.57r = -1.02 + 0.00 -51.442 + -0.57r = -1.02 Add '51.442' to each side of the equation. -51.442 + 51.442 + -0.57r = -1.02 + 51.442 Combine like terms: -51.442 + 51.442 = 0.000 0.000 + -0.57r = -1.02 + 51.442 -0.57r = -1.02 + 51.442 Combine like terms: -1.02 + 51.442 = 50.422 -0.57r = 50.422 Divide each side by '-0.57'. r = -88.45964912 Simplifying r = -88.45964912
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