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Simplifying 6r + 5(r + 6) + -3(s + -5) = 0 Reorder the terms: 6r + 5(6 + r) + -3(s + -5) = 0 6r + (6 * 5 + r * 5) + -3(s + -5) = 0 6r + (30 + 5r) + -3(s + -5) = 0 Reorder the terms: 6r + 30 + 5r + -3(-5 + s) = 0 6r + 30 + 5r + (-5 * -3 + s * -3) = 0 6r + 30 + 5r + (15 + -3s) = 0 Reorder the terms: 30 + 15 + 6r + 5r + -3s = 0 Combine like terms: 30 + 15 = 45 45 + 6r + 5r + -3s = 0 Combine like terms: 6r + 5r = 11r 45 + 11r + -3s = 0 Solving 45 + 11r + -3s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + 11r + -45 + -3s = 0 + -45 Reorder the terms: 45 + -45 + 11r + -3s = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 11r + -3s = 0 + -45 11r + -3s = 0 + -45 Combine like terms: 0 + -45 = -45 11r + -3s = -45 Add '3s' to each side of the equation. 11r + -3s + 3s = -45 + 3s Combine like terms: -3s + 3s = 0 11r + 0 = -45 + 3s 11r = -45 + 3s Divide each side by '11'. r = -4.090909091 + 0.2727272727s Simplifying r = -4.090909091 + 0.2727272727s
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