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Simplifying 8(2.4r + -3.1t) + -6(1.5r + 2.4t) = 0 (2.4r * 8 + -3.1t * 8) + -6(1.5r + 2.4t) = 0 (19.2r + -24.8t) + -6(1.5r + 2.4t) = 0 19.2r + -24.8t + (1.5r * -6 + 2.4t * -6) = 0 19.2r + -24.8t + (-9r + -14.4t) = 0 Reorder the terms: 19.2r + -9r + -24.8t + -14.4t = 0 Combine like terms: 19.2r + -9r = 10.2r 10.2r + -24.8t + -14.4t = 0 Combine like terms: -24.8t + -14.4t = -39.2t 10.2r + -39.2t = 0 Solving 10.2r + -39.2t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '39.2t' to each side of the equation. 10.2r + -39.2t + 39.2t = 0 + 39.2t Combine like terms: -39.2t + 39.2t = 0.0 10.2r + 0.0 = 0 + 39.2t 10.2r = 0 + 39.2t Remove the zero: 10.2r = 39.2t Divide each side by '10.2'. r = 3.843137255t Simplifying r = 3.843137255t
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