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Simplifying 2(r + s) + 5(2r + -1s) + -3 = 3r + -6 (r * 2 + s * 2) + 5(2r + -1s) + -3 = 3r + -6 (2r + 2s) + 5(2r + -1s) + -3 = 3r + -6 2r + 2s + (2r * 5 + -1s * 5) + -3 = 3r + -6 2r + 2s + (10r + -5s) + -3 = 3r + -6 Reorder the terms: -3 + 2r + 10r + 2s + -5s = 3r + -6 Combine like terms: 2r + 10r = 12r -3 + 12r + 2s + -5s = 3r + -6 Combine like terms: 2s + -5s = -3s -3 + 12r + -3s = 3r + -6 Reorder the terms: -3 + 12r + -3s = -6 + 3r Solving -3 + 12r + -3s = -6 + 3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3r' to each side of the equation. -3 + 12r + -3r + -3s = -6 + 3r + -3r Combine like terms: 12r + -3r = 9r -3 + 9r + -3s = -6 + 3r + -3r Combine like terms: 3r + -3r = 0 -3 + 9r + -3s = -6 + 0 -3 + 9r + -3s = -6 Add '3' to each side of the equation. -3 + 9r + 3 + -3s = -6 + 3 Reorder the terms: -3 + 3 + 9r + -3s = -6 + 3 Combine like terms: -3 + 3 = 0 0 + 9r + -3s = -6 + 3 9r + -3s = -6 + 3 Combine like terms: -6 + 3 = -3 9r + -3s = -3 Add '3s' to each side of the equation. 9r + -3s + 3s = -3 + 3s Combine like terms: -3s + 3s = 0 9r + 0 = -3 + 3s 9r = -3 + 3s Divide each side by '9'. r = -0.3333333333 + 0.3333333333s Simplifying r = -0.3333333333 + 0.3333333333s
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