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Simplifying 2(q) + 5(1 + -1q) = 6q + 1(1 + -1q) 2q + (1 * 5 + -1q * 5) = 6q + 1(1 + -1q) 2q + (5 + -5q) = 6q + 1(1 + -1q) Reorder the terms: 5 + 2q + -5q = 6q + 1(1 + -1q) Combine like terms: 2q + -5q = -3q 5 + -3q = 6q + 1(1 + -1q) 5 + -3q = 6q + (1 * 1 + -1q * 1) 5 + -3q = 6q + (1 + -1q) Reorder the terms: 5 + -3q = 1 + 6q + -1q Combine like terms: 6q + -1q = 5q 5 + -3q = 1 + 5q Solving 5 + -3q = 1 + 5q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-5q' to each side of the equation. 5 + -3q + -5q = 1 + 5q + -5q Combine like terms: -3q + -5q = -8q 5 + -8q = 1 + 5q + -5q Combine like terms: 5q + -5q = 0 5 + -8q = 1 + 0 5 + -8q = 1 Add '-5' to each side of the equation. 5 + -5 + -8q = 1 + -5 Combine like terms: 5 + -5 = 0 0 + -8q = 1 + -5 -8q = 1 + -5 Combine like terms: 1 + -5 = -4 -8q = -4 Divide each side by '-8'. q = 0.5 Simplifying q = 0.5
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