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Simplifying -1(3r + -5s + 7t) + -1(10s + -4r + -3t) = 0 (3r * -1 + -5s * -1 + 7t * -1) + -1(10s + -4r + -3t) = 0 (-3r + 5s + -7t) + -1(10s + -4r + -3t) = 0 Reorder the terms: -3r + 5s + -7t + -1(-4r + 10s + -3t) = 0 -3r + 5s + -7t + (-4r * -1 + 10s * -1 + -3t * -1) = 0 -3r + 5s + -7t + (4r + -10s + 3t) = 0 Reorder the terms: -3r + 4r + 5s + -10s + -7t + 3t = 0 Combine like terms: -3r + 4r = 1r 1r + 5s + -10s + -7t + 3t = 0 Combine like terms: 5s + -10s = -5s 1r + -5s + -7t + 3t = 0 Combine like terms: -7t + 3t = -4t 1r + -5s + -4t = 0 Solving 1r + -5s + -4t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5s' to each side of the equation. 1r + -5s + 5s + -4t = 0 + 5s Combine like terms: -5s + 5s = 0 1r + 0 + -4t = 0 + 5s 1r + -4t = 0 + 5s Remove the zero: 1r + -4t = 5s Add '4t' to each side of the equation. 1r + -4t + 4t = 5s + 4t Combine like terms: -4t + 4t = 0 1r + 0 = 5s + 4t 1r = 5s + 4t Divide each side by '1'. r = 5s + 4t Simplifying r = 5s + 4t
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