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Simplifying 8(4q + 1) = 3(9q + 16) Reorder the terms: 8(1 + 4q) = 3(9q + 16) (1 * 8 + 4q * 8) = 3(9q + 16) (8 + 32q) = 3(9q + 16) Reorder the terms: 8 + 32q = 3(16 + 9q) 8 + 32q = (16 * 3 + 9q * 3) 8 + 32q = (48 + 27q) Solving 8 + 32q = 48 + 27q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-27q' to each side of the equation. 8 + 32q + -27q = 48 + 27q + -27q Combine like terms: 32q + -27q = 5q 8 + 5q = 48 + 27q + -27q Combine like terms: 27q + -27q = 0 8 + 5q = 48 + 0 8 + 5q = 48 Add '-8' to each side of the equation. 8 + -8 + 5q = 48 + -8 Combine like terms: 8 + -8 = 0 0 + 5q = 48 + -8 5q = 48 + -8 Combine like terms: 48 + -8 = 40 5q = 40 Divide each side by '5'. q = 8 Simplifying q = 8
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