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Simplifying (4r + 3s + -1t) + -1(r + 2s + -5t) = 0 Remove parenthesis around (4r + 3s + -1t) 4r + 3s + -1t + -1(r + 2s + -5t) = 0 4r + 3s + -1t + (r * -1 + 2s * -1 + -5t * -1) = 0 4r + 3s + -1t + (-1r + -2s + 5t) = 0 Reorder the terms: 4r + -1r + 3s + -2s + -1t + 5t = 0 Combine like terms: 4r + -1r = 3r 3r + 3s + -2s + -1t + 5t = 0 Combine like terms: 3s + -2s = 1s 3r + 1s + -1t + 5t = 0 Combine like terms: -1t + 5t = 4t 3r + 1s + 4t = 0 Solving 3r + 1s + 4t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 3r + 1s + -1s + 4t = 0 + -1s Combine like terms: 1s + -1s = 0 3r + 0 + 4t = 0 + -1s 3r + 4t = 0 + -1s Remove the zero: 3r + 4t = -1s Add '-4t' to each side of the equation. 3r + 4t + -4t = -1s + -4t Combine like terms: 4t + -4t = 0 3r + 0 = -1s + -4t 3r = -1s + -4t Divide each side by '3'. r = -0.3333333333s + -1.333333333t Simplifying r = -0.3333333333s + -1.333333333t
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