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Simplifying 5[2q + 1] + 7[4q + 2] = 0 Reorder the terms: 5[1 + 2q] + 7[4q + 2] = 0 [1 * 5 + 2q * 5] + 7[4q + 2] = 0 [5 + 10q] + 7[4q + 2] = 0 Reorder the terms: 5 + 10q + 7[2 + 4q] = 0 5 + 10q + [2 * 7 + 4q * 7] = 0 5 + 10q + [14 + 28q] = 0 Reorder the terms: 5 + 14 + 10q + 28q = 0 Combine like terms: 5 + 14 = 19 19 + 10q + 28q = 0 Combine like terms: 10q + 28q = 38q 19 + 38q = 0 Solving 19 + 38q = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 38q = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 38q = 0 + -19 38q = 0 + -19 Combine like terms: 0 + -19 = -19 38q = -19 Divide each side by '38'. q = -0.5 Simplifying q = -0.5
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