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Simplifying 3(r + s) + 4(2r + -1s) = 0 (r * 3 + s * 3) + 4(2r + -1s) = 0 (3r + 3s) + 4(2r + -1s) = 0 3r + 3s + (2r * 4 + -1s * 4) = 0 3r + 3s + (8r + -4s) = 0 Reorder the terms: 3r + 8r + 3s + -4s = 0 Combine like terms: 3r + 8r = 11r 11r + 3s + -4s = 0 Combine like terms: 3s + -4s = -1s 11r + -1s = 0 Solving 11r + -1s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add 's' to each side of the equation. 11r + -1s + s = 0 + s Combine like terms: -1s + s = 0 11r + 0 = 0 + s 11r = 0 + s Remove the zero: 11r = s Divide each side by '11'. r = 0.09090909091s Simplifying r = 0.09090909091s
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