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Simplifying 0.03(3z + 5) + 12.9 = 0.6(3z + -6) Reorder the terms: 0.03(5 + 3z) + 12.9 = 0.6(3z + -6) (5 * 0.03 + 3z * 0.03) + 12.9 = 0.6(3z + -6) (0.15 + 0.09z) + 12.9 = 0.6(3z + -6) Reorder the terms: 0.15 + 12.9 + 0.09z = 0.6(3z + -6) Combine like terms: 0.15 + 12.9 = 13.05 13.05 + 0.09z = 0.6(3z + -6) Reorder the terms: 13.05 + 0.09z = 0.6(-6 + 3z) 13.05 + 0.09z = (-6 * 0.6 + 3z * 0.6) 13.05 + 0.09z = (-3.6 + 1.8z) Solving 13.05 + 0.09z = -3.6 + 1.8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.8z' to each side of the equation. 13.05 + 0.09z + -1.8z = -3.6 + 1.8z + -1.8z Combine like terms: 0.09z + -1.8z = -1.71z 13.05 + -1.71z = -3.6 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 13.05 + -1.71z = -3.6 + 0.0 13.05 + -1.71z = -3.6 Add '-13.05' to each side of the equation. 13.05 + -13.05 + -1.71z = -3.6 + -13.05 Combine like terms: 13.05 + -13.05 = 0.00 0.00 + -1.71z = -3.6 + -13.05 -1.71z = -3.6 + -13.05 Combine like terms: -3.6 + -13.05 = -16.65 -1.71z = -16.65 Divide each side by '-1.71'. z = 9.736842105 Simplifying z = 9.736842105
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