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Simplifying 100q + -80(1 + -1q) = -90q + -50(1 + -1q) 100q + (1 * -80 + -1q * -80) = -90q + -50(1 + -1q) 100q + (-80 + 80q) = -90q + -50(1 + -1q) Reorder the terms: -80 + 100q + 80q = -90q + -50(1 + -1q) Combine like terms: 100q + 80q = 180q -80 + 180q = -90q + -50(1 + -1q) -80 + 180q = -90q + (1 * -50 + -1q * -50) -80 + 180q = -90q + (-50 + 50q) Reorder the terms: -80 + 180q = -50 + -90q + 50q Combine like terms: -90q + 50q = -40q -80 + 180q = -50 + -40q Solving -80 + 180q = -50 + -40q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '40q' to each side of the equation. -80 + 180q + 40q = -50 + -40q + 40q Combine like terms: 180q + 40q = 220q -80 + 220q = -50 + -40q + 40q Combine like terms: -40q + 40q = 0 -80 + 220q = -50 + 0 -80 + 220q = -50 Add '80' to each side of the equation. -80 + 80 + 220q = -50 + 80 Combine like terms: -80 + 80 = 0 0 + 220q = -50 + 80 220q = -50 + 80 Combine like terms: -50 + 80 = 30 220q = 30 Divide each side by '220'. q = 0.1363636364 Simplifying q = 0.1363636364
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