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Simplifying -100q + 90(1 + -1q) = 80q + -70(1 + -1q) -100q + (1 * 90 + -1q * 90) = 80q + -70(1 + -1q) -100q + (90 + -90q) = 80q + -70(1 + -1q) Reorder the terms: 90 + -100q + -90q = 80q + -70(1 + -1q) Combine like terms: -100q + -90q = -190q 90 + -190q = 80q + -70(1 + -1q) 90 + -190q = 80q + (1 * -70 + -1q * -70) 90 + -190q = 80q + (-70 + 70q) Reorder the terms: 90 + -190q = -70 + 80q + 70q Combine like terms: 80q + 70q = 150q 90 + -190q = -70 + 150q Solving 90 + -190q = -70 + 150q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-150q' to each side of the equation. 90 + -190q + -150q = -70 + 150q + -150q Combine like terms: -190q + -150q = -340q 90 + -340q = -70 + 150q + -150q Combine like terms: 150q + -150q = 0 90 + -340q = -70 + 0 90 + -340q = -70 Add '-90' to each side of the equation. 90 + -90 + -340q = -70 + -90 Combine like terms: 90 + -90 = 0 0 + -340q = -70 + -90 -340q = -70 + -90 Combine like terms: -70 + -90 = -160 -340q = -160 Divide each side by '-340'. q = 0.4705882353 Simplifying q = 0.4705882353
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