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Simplifying 3(7q + -1r) + -4(8s + -1t) = 0 (7q * 3 + -1r * 3) + -4(8s + -1t) = 0 (21q + -3r) + -4(8s + -1t) = 0 21q + -3r + (8s * -4 + -1t * -4) = 0 21q + -3r + (-32s + 4t) = 0 Solving 21q + -3r + -32s + 4t = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3r' to each side of the equation. 21q + -3r + -32s + 3r + 4t = 0 + 3r Reorder the terms: 21q + -3r + 3r + -32s + 4t = 0 + 3r Combine like terms: -3r + 3r = 0 21q + 0 + -32s + 4t = 0 + 3r 21q + -32s + 4t = 0 + 3r Remove the zero: 21q + -32s + 4t = 3r Add '32s' to each side of the equation. 21q + -32s + 32s + 4t = 3r + 32s Combine like terms: -32s + 32s = 0 21q + 0 + 4t = 3r + 32s 21q + 4t = 3r + 32s Add '-4t' to each side of the equation. 21q + 4t + -4t = 3r + 32s + -4t Combine like terms: 4t + -4t = 0 21q + 0 = 3r + 32s + -4t 21q = 3r + 32s + -4t Divide each side by '21'. q = 0.1428571429r + 1.523809524s + -0.1904761905t Simplifying q = 0.1428571429r + 1.523809524s + -0.1904761905t
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