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Simplifying 0.3(3z + 6) + 13.2 = 0.5(3z + -6) Reorder the terms: 0.3(6 + 3z) + 13.2 = 0.5(3z + -6) (6 * 0.3 + 3z * 0.3) + 13.2 = 0.5(3z + -6) (1.8 + 0.9z) + 13.2 = 0.5(3z + -6) Reorder the terms: 1.8 + 13.2 + 0.9z = 0.5(3z + -6) Combine like terms: 1.8 + 13.2 = 15 15 + 0.9z = 0.5(3z + -6) Reorder the terms: 15 + 0.9z = 0.5(-6 + 3z) 15 + 0.9z = (-6 * 0.5 + 3z * 0.5) 15 + 0.9z = (-3 + 1.5z) Solving 15 + 0.9z = -3 + 1.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.5z' to each side of the equation. 15 + 0.9z + -1.5z = -3 + 1.5z + -1.5z Combine like terms: 0.9z + -1.5z = -0.6z 15 + -0.6z = -3 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 15 + -0.6z = -3 + 0.0 15 + -0.6z = -3 Add '-15' to each side of the equation. 15 + -15 + -0.6z = -3 + -15 Combine like terms: 15 + -15 = 0 0 + -0.6z = -3 + -15 -0.6z = -3 + -15 Combine like terms: -3 + -15 = -18 -0.6z = -18 Divide each side by '-0.6'. z = 30 Simplifying z = 30
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