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Simplifying 8(3q + 1) + -4(1 + 4q) = 0 Reorder the terms: 8(1 + 3q) + -4(1 + 4q) = 0 (1 * 8 + 3q * 8) + -4(1 + 4q) = 0 (8 + 24q) + -4(1 + 4q) = 0 8 + 24q + (1 * -4 + 4q * -4) = 0 8 + 24q + (-4 + -16q) = 0 Reorder the terms: 8 + -4 + 24q + -16q = 0 Combine like terms: 8 + -4 = 4 4 + 24q + -16q = 0 Combine like terms: 24q + -16q = 8q 4 + 8q = 0 Solving 4 + 8q = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 8q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8q = 0 + -4 8q = 0 + -4 Combine like terms: 0 + -4 = -4 8q = -4 Divide each side by '8'. q = -0.5 Simplifying q = -0.5
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