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Simplifying 0.1q + -0.2(3q + 4) = -0.3(5q + 3) Reorder the terms: 0.1q + -0.2(4 + 3q) = -0.3(5q + 3) 0.1q + (4 * -0.2 + 3q * -0.2) = -0.3(5q + 3) 0.1q + (-0.8 + -0.6q) = -0.3(5q + 3) Reorder the terms: -0.8 + 0.1q + -0.6q = -0.3(5q + 3) Combine like terms: 0.1q + -0.6q = -0.5q -0.8 + -0.5q = -0.3(5q + 3) Reorder the terms: -0.8 + -0.5q = -0.3(3 + 5q) -0.8 + -0.5q = (3 * -0.3 + 5q * -0.3) -0.8 + -0.5q = (-0.9 + -1.5q) Solving -0.8 + -0.5q = -0.9 + -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. -0.8 + -0.5q + 1.5q = -0.9 + -1.5q + 1.5q Combine like terms: -0.5q + 1.5q = 1q -0.8 + 1q = -0.9 + -1.5q + 1.5q Combine like terms: -1.5q + 1.5q = 0.0 -0.8 + 1q = -0.9 + 0.0 -0.8 + 1q = -0.9 Add '0.8' to each side of the equation. -0.8 + 0.8 + 1q = -0.9 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1q = -0.9 + 0.8 1q = -0.9 + 0.8 Combine like terms: -0.9 + 0.8 = -0.1 1q = -0.1 Divide each side by '1'. q = -0.1 Simplifying q = -0.1
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