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Simplifying (6t + -3r + 2w) + -1(-3t + -1r + 4w) = 0 Reorder the terms: (-3r + 6t + 2w) + -1(-3t + -1r + 4w) = 0 Remove parenthesis around (-3r + 6t + 2w) -3r + 6t + 2w + -1(-3t + -1r + 4w) = 0 Reorder the terms: -3r + 6t + 2w + -1(-1r + -3t + 4w) = 0 -3r + 6t + 2w + (-1r * -1 + -3t * -1 + 4w * -1) = 0 -3r + 6t + 2w + (1r + 3t + -4w) = 0 Reorder the terms: -3r + 1r + 6t + 3t + 2w + -4w = 0 Combine like terms: -3r + 1r = -2r -2r + 6t + 3t + 2w + -4w = 0 Combine like terms: 6t + 3t = 9t -2r + 9t + 2w + -4w = 0 Combine like terms: 2w + -4w = -2w -2r + 9t + -2w = 0 Solving -2r + 9t + -2w = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9t' to each side of the equation. -2r + 9t + -9t + -2w = 0 + -9t Combine like terms: 9t + -9t = 0 -2r + 0 + -2w = 0 + -9t -2r + -2w = 0 + -9t Remove the zero: -2r + -2w = -9t Add '2w' to each side of the equation. -2r + -2w + 2w = -9t + 2w Combine like terms: -2w + 2w = 0 -2r + 0 = -9t + 2w -2r = -9t + 2w Divide each side by '-2'. r = 4.5t + -1w Simplifying r = 4.5t + -1w
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