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Simplifying 0.5(4z + 5) + 6.5 = 0.6(4z + -5) Reorder the terms: 0.5(5 + 4z) + 6.5 = 0.6(4z + -5) (5 * 0.5 + 4z * 0.5) + 6.5 = 0.6(4z + -5) (2.5 + 2z) + 6.5 = 0.6(4z + -5) Reorder the terms: 2.5 + 6.5 + 2z = 0.6(4z + -5) Combine like terms: 2.5 + 6.5 = 9 9 + 2z = 0.6(4z + -5) Reorder the terms: 9 + 2z = 0.6(-5 + 4z) 9 + 2z = (-5 * 0.6 + 4z * 0.6) 9 + 2z = (-3 + 2.4z) Solving 9 + 2z = -3 + 2.4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.4z' to each side of the equation. 9 + 2z + -2.4z = -3 + 2.4z + -2.4z Combine like terms: 2z + -2.4z = -0.4z 9 + -0.4z = -3 + 2.4z + -2.4z Combine like terms: 2.4z + -2.4z = 0.0 9 + -0.4z = -3 + 0.0 9 + -0.4z = -3 Add '-9' to each side of the equation. 9 + -9 + -0.4z = -3 + -9 Combine like terms: 9 + -9 = 0 0 + -0.4z = -3 + -9 -0.4z = -3 + -9 Combine like terms: -3 + -9 = -12 -0.4z = -12 Divide each side by '-0.4'. z = 30 Simplifying z = 30

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