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Simplifying 3(2q + r) + 5(4q + -7r) = 0 (2q * 3 + r * 3) + 5(4q + -7r) = 0 (6q + 3r) + 5(4q + -7r) = 0 6q + 3r + (4q * 5 + -7r * 5) = 0 6q + 3r + (20q + -35r) = 0 Reorder the terms: 6q + 20q + 3r + -35r = 0 Combine like terms: 6q + 20q = 26q 26q + 3r + -35r = 0 Combine like terms: 3r + -35r = -32r 26q + -32r = 0 Solving 26q + -32r = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '32r' to each side of the equation. 26q + -32r + 32r = 0 + 32r Combine like terms: -32r + 32r = 0 26q + 0 = 0 + 32r 26q = 0 + 32r Remove the zero: 26q = 32r Divide each side by '26'. q = 1.230769231r Simplifying q = 1.230769231r
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