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Simplifying 0.142857(14 + -7q) + -2 = -2(0.5q + 3) + 6 (14 * 0.142857 + -7q * 0.142857) + -2 = -2(0.5q + 3) + 6 (1.999998 + -0.999999q) + -2 = -2(0.5q + 3) + 6 Reorder the terms: 1.999998 + -2 + -0.999999q = -2(0.5q + 3) + 6 Combine like terms: 1.999998 + -2 = -0.000002 -0.000002 + -0.999999q = -2(0.5q + 3) + 6 Reorder the terms: -0.000002 + -0.999999q = -2(3 + 0.5q) + 6 -0.000002 + -0.999999q = (3 * -2 + 0.5q * -2) + 6 -0.000002 + -0.999999q = (-6 + -1q) + 6 Reorder the terms: -0.000002 + -0.999999q = -6 + 6 + -1q Combine like terms: -6 + 6 = 0 -0.000002 + -0.999999q = 0 + -1q -0.000002 + -0.999999q = -1q Solving -0.000002 + -0.999999q = -1q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add 'q' to each side of the equation. -0.000002 + -0.999999q + q = -1q + q Combine like terms: -0.999999q + q = 0.000001q -0.000002 + 0.000001q = -1q + q Combine like terms: -1q + q = 0 -0.000002 + 0.000001q = 0 Add '0.000002' to each side of the equation. -0.000002 + 0.000002 + 0.000001q = 0 + 0.000002 Combine like terms: -0.000002 + 0.000002 = 0.000000 0.000000 + 0.000001q = 0 + 0.000002 0.000001q = 0 + 0.000002 Combine like terms: 0 + 0.000002 = 0.000002 0.000001q = 0.000002 Divide each side by '0.000001'. q = 2 Simplifying q = 2
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