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Simplifying 0.5(10z + 20) + -5 = 0.2(50z + 50) Reorder the terms: 0.5(20 + 10z) + -5 = 0.2(50z + 50) (20 * 0.5 + 10z * 0.5) + -5 = 0.2(50z + 50) (10 + 5z) + -5 = 0.2(50z + 50) Reorder the terms: 10 + -5 + 5z = 0.2(50z + 50) Combine like terms: 10 + -5 = 5 5 + 5z = 0.2(50z + 50) Reorder the terms: 5 + 5z = 0.2(50 + 50z) 5 + 5z = (50 * 0.2 + 50z * 0.2) 5 + 5z = (10 + 10z) Solving 5 + 5z = 10 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. 5 + 5z + -10z = 10 + 10z + -10z Combine like terms: 5z + -10z = -5z 5 + -5z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 5 + -5z = 10 + 0 5 + -5z = 10 Add '-5' to each side of the equation. 5 + -5 + -5z = 10 + -5 Combine like terms: 5 + -5 = 0 0 + -5z = 10 + -5 -5z = 10 + -5 Combine like terms: 10 + -5 = 5 -5z = 5 Divide each side by '-5'. z = -1 Simplifying z = -1
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