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Simplifying (5r + 2s + -1t) + -1(-3r + -1s + 6t) = 0 Remove parenthesis around (5r + 2s + -1t) 5r + 2s + -1t + -1(-3r + -1s + 6t) = 0 5r + 2s + -1t + (-3r * -1 + -1s * -1 + 6t * -1) = 0 5r + 2s + -1t + (3r + 1s + -6t) = 0 Reorder the terms: 5r + 3r + 2s + 1s + -1t + -6t = 0 Combine like terms: 5r + 3r = 8r 8r + 2s + 1s + -1t + -6t = 0 Combine like terms: 2s + 1s = 3s 8r + 3s + -1t + -6t = 0 Combine like terms: -1t + -6t = -7t 8r + 3s + -7t = 0 Solving 8r + 3s + -7t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3s' to each side of the equation. 8r + 3s + -3s + -7t = 0 + -3s Combine like terms: 3s + -3s = 0 8r + 0 + -7t = 0 + -3s 8r + -7t = 0 + -3s Remove the zero: 8r + -7t = -3s Add '7t' to each side of the equation. 8r + -7t + 7t = -3s + 7t Combine like terms: -7t + 7t = 0 8r + 0 = -3s + 7t 8r = -3s + 7t Divide each side by '8'. r = -0.375s + 0.875t Simplifying r = -0.375s + 0.875t
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