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Simplifying 0.4(3z + 5) + 6.4 = 0.6(3z + -6) Reorder the terms: 0.4(5 + 3z) + 6.4 = 0.6(3z + -6) (5 * 0.4 + 3z * 0.4) + 6.4 = 0.6(3z + -6) (2 + 1.2z) + 6.4 = 0.6(3z + -6) Reorder the terms: 2 + 6.4 + 1.2z = 0.6(3z + -6) Combine like terms: 2 + 6.4 = 8.4 8.4 + 1.2z = 0.6(3z + -6) Reorder the terms: 8.4 + 1.2z = 0.6(-6 + 3z) 8.4 + 1.2z = (-6 * 0.6 + 3z * 0.6) 8.4 + 1.2z = (-3.6 + 1.8z) Solving 8.4 + 1.2z = -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. 8.4 + 1.2z + -1.8z = -3.6 + 1.8z + -1.8z Combine like terms: 1.2z + -1.8z = -0.6z 8.4 + -0.6z = -3.6 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 8.4 + -0.6z = -3.6 + 0.0 8.4 + -0.6z = -3.6 Add '-8.4' to each side of the equation. 8.4 + -8.4 + -0.6z = -3.6 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + -0.6z = -3.6 + -8.4 -0.6z = -3.6 + -8.4 Combine like terms: -3.6 + -8.4 = -12 -0.6z = -12 Divide each side by '-0.6'. z = 20 Simplifying z = 20
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