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Simplifying 7(3r + -2w) + (5r + 3w) = 0 (3r * 7 + -2w * 7) + (5r + 3w) = 0 (21r + -14w) + (5r + 3w) = 0 Remove parenthesis around (5r + 3w) 21r + -14w + 5r + 3w = 0 Reorder the terms: 21r + 5r + -14w + 3w = 0 Combine like terms: 21r + 5r = 26r 26r + -14w + 3w = 0 Combine like terms: -14w + 3w = -11w 26r + -11w = 0 Solving 26r + -11w = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11w' to each side of the equation. 26r + -11w + 11w = 0 + 11w Combine like terms: -11w + 11w = 0 26r + 0 = 0 + 11w 26r = 0 + 11w Remove the zero: 26r = 11w Divide each side by '26'. r = 0.4230769231w Simplifying r = 0.4230769231w
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