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Simplifying (-4r + 2s + -1t) + -1(2r + s + -5t) = 0 Remove parenthesis around (-4r + 2s + -1t) -4r + 2s + -1t + -1(2r + s + -5t) = 0 -4r + 2s + -1t + (2r * -1 + s * -1 + -5t * -1) = 0 -4r + 2s + -1t + (-2r + -1s + 5t) = 0 Reorder the terms: -4r + -2r + 2s + -1s + -1t + 5t = 0 Combine like terms: -4r + -2r = -6r -6r + 2s + -1s + -1t + 5t = 0 Combine like terms: 2s + -1s = 1s -6r + 1s + -1t + 5t = 0 Combine like terms: -1t + 5t = 4t -6r + 1s + 4t = 0 Solving -6r + 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. -6r + 1s + -1s + 4t = 0 + -1s Combine like terms: 1s + -1s = 0 -6r + 0 + 4t = 0 + -1s -6r + 4t = 0 + -1s Remove the zero: -6r + 4t = -1s Add '-4t' to each side of the equation. -6r + 4t + -4t = -1s + -4t Combine like terms: 4t + -4t = 0 -6r + 0 = -1s + -4t -6r = -1s + -4t Divide each side by '-6'. r = 0.1666666667s + 0.6666666667t Simplifying r = 0.1666666667s + 0.6666666667t
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