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Simplifying (8r + 3t) + -1[2 + -1(t + 3r)] = 0 Remove parenthesis around (8r + 3t) 8r + 3t + -1[2 + -1(t + 3r)] = 0 Reorder the terms: 8r + 3t + -1[2 + -1(3r + t)] = 0 8r + 3t + -1[2 + (3r * -1 + t * -1)] = 0 8r + 3t + -1[2 + (-3r + -1t)] = 0 8r + 3t + [2 * -1 + -3r * -1 + -1t * -1] = 0 8r + 3t + [-2 + 3r + 1t] = 0 Reorder the terms: -2 + 8r + 3r + 3t + 1t = 0 Combine like terms: 8r + 3r = 11r -2 + 11r + 3t + 1t = 0 Combine like terms: 3t + 1t = 4t -2 + 11r + 4t = 0 Solving -2 + 11r + 4t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 11r + 2 + 4t = 0 + 2 Reorder the terms: -2 + 2 + 11r + 4t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 11r + 4t = 0 + 2 11r + 4t = 0 + 2 Combine like terms: 0 + 2 = 2 11r + 4t = 2 Add '-4t' to each side of the equation. 11r + 4t + -4t = 2 + -4t Combine like terms: 4t + -4t = 0 11r + 0 = 2 + -4t 11r = 2 + -4t Divide each side by '11'. r = 0.1818181818 + -0.3636363636t Simplifying r = 0.1818181818 + -0.3636363636t
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