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Simplifying 1.5(2q + -4) + -2 = 0.5(3q + 8) Reorder the terms: 1.5(-4 + 2q) + -2 = 0.5(3q + 8) (-4 * 1.5 + 2q * 1.5) + -2 = 0.5(3q + 8) (-6 + 3q) + -2 = 0.5(3q + 8) Reorder the terms: -6 + -2 + 3q = 0.5(3q + 8) Combine like terms: -6 + -2 = -8 -8 + 3q = 0.5(3q + 8) Reorder the terms: -8 + 3q = 0.5(8 + 3q) -8 + 3q = (8 * 0.5 + 3q * 0.5) -8 + 3q = (4 + 1.5q) Solving -8 + 3q = 4 + 1.5q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.5q' to each side of the equation. -8 + 3q + -1.5q = 4 + 1.5q + -1.5q Combine like terms: 3q + -1.5q = 1.5q -8 + 1.5q = 4 + 1.5q + -1.5q Combine like terms: 1.5q + -1.5q = 0.0 -8 + 1.5q = 4 + 0.0 -8 + 1.5q = 4 Add '8' to each side of the equation. -8 + 8 + 1.5q = 4 + 8 Combine like terms: -8 + 8 = 0 0 + 1.5q = 4 + 8 1.5q = 4 + 8 Combine like terms: 4 + 8 = 12 1.5q = 12 Divide each side by '1.5'. q = 8 Simplifying q = 8
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