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Simplifying 0.4(4z + 7) * 10.2 = 0.5(4z + -6) Reorder the terms: 0.4(7 + 4z) * 10.2 = 0.5(4z + -6) Reorder the terms for easier multiplication: 0.4 * 10.2(7 + 4z) = 0.5(4z + -6) Multiply 0.4 * 10.2 4.08(7 + 4z) = 0.5(4z + -6) (7 * 4.08 + 4z * 4.08) = 0.5(4z + -6) (28.56 + 16.32z) = 0.5(4z + -6) Reorder the terms: 28.56 + 16.32z = 0.5(-6 + 4z) 28.56 + 16.32z = (-6 * 0.5 + 4z * 0.5) 28.56 + 16.32z = (-3 + 2z) Solving 28.56 + 16.32z = -3 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 28.56 + 16.32z + -2z = -3 + 2z + -2z Combine like terms: 16.32z + -2z = 14.32z 28.56 + 14.32z = -3 + 2z + -2z Combine like terms: 2z + -2z = 0 28.56 + 14.32z = -3 + 0 28.56 + 14.32z = -3 Add '-28.56' to each side of the equation. 28.56 + -28.56 + 14.32z = -3 + -28.56 Combine like terms: 28.56 + -28.56 = 0.00 0.00 + 14.32z = -3 + -28.56 14.32z = -3 + -28.56 Combine like terms: -3 + -28.56 = -31.56 14.32z = -31.56 Divide each side by '14.32'. z = -2.203910615 Simplifying z = -2.203910615
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