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Simplifying (4r + -1s) + -1(r + 2s) + (3r + -1s) = 0 Remove parenthesis around (4r + -1s) 4r + -1s + -1(r + 2s) + (3r + -1s) = 0 4r + -1s + (r * -1 + 2s * -1) + (3r + -1s) = 0 4r + -1s + (-1r + -2s) + (3r + -1s) = 0 Remove parenthesis around (3r + -1s) 4r + -1s + -1r + -2s + 3r + -1s = 0 Reorder the terms: 4r + -1r + 3r + -1s + -2s + -1s = 0 Combine like terms: 4r + -1r = 3r 3r + 3r + -1s + -2s + -1s = 0 Combine like terms: 3r + 3r = 6r 6r + -1s + -2s + -1s = 0 Combine like terms: -1s + -2s = -3s 6r + -3s + -1s = 0 Combine like terms: -3s + -1s = -4s 6r + -4s = 0 Solving 6r + -4s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 6r + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 6r + 0 = 0 + 4s 6r = 0 + 4s Remove the zero: 6r = 4s Divide each side by '6'. r = 0.6666666667s Simplifying r = 0.6666666667s
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