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Simplifying (6r + -7s + 8t) + -1(2r + -3s + 4t) = 0 Remove parenthesis around (6r + -7s + 8t) 6r + -7s + 8t + -1(2r + -3s + 4t) = 0 6r + -7s + 8t + (2r * -1 + -3s * -1 + 4t * -1) = 0 6r + -7s + 8t + (-2r + 3s + -4t) = 0 Reorder the terms: 6r + -2r + -7s + 3s + 8t + -4t = 0 Combine like terms: 6r + -2r = 4r 4r + -7s + 3s + 8t + -4t = 0 Combine like terms: -7s + 3s = -4s 4r + -4s + 8t + -4t = 0 Combine like terms: 8t + -4t = 4t 4r + -4s + 4t = 0 Solving 4r + -4s + 4t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 4r + -4s + 4s + 4t = 0 + 4s Combine like terms: -4s + 4s = 0 4r + 0 + 4t = 0 + 4s 4r + 4t = 0 + 4s Remove the zero: 4r + 4t = 4s Add '-4t' to each side of the equation. 4r + 4t + -4t = 4s + -4t Combine like terms: 4t + -4t = 0 4r + 0 = 4s + -4t 4r = 4s + -4t Divide each side by '4'. r = s + -1t Simplifying r = s + -1t
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