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Simplifying 0.125(z + 4) = -0.5(z + -5) Reorder the terms: 0.125(4 + z) = -0.5(z + -5) (4 * 0.125 + z * 0.125) = -0.5(z + -5) (0.5 + 0.125z) = -0.5(z + -5) Reorder the terms: 0.5 + 0.125z = -0.5(-5 + z) 0.5 + 0.125z = (-5 * -0.5 + z * -0.5) 0.5 + 0.125z = (2.5 + -0.5z) Solving 0.5 + 0.125z = 2.5 + -0.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5z' to each side of the equation. 0.5 + 0.125z + 0.5z = 2.5 + -0.5z + 0.5z Combine like terms: 0.125z + 0.5z = 0.625z 0.5 + 0.625z = 2.5 + -0.5z + 0.5z Combine like terms: -0.5z + 0.5z = 0.0 0.5 + 0.625z = 2.5 + 0.0 0.5 + 0.625z = 2.5 Add '-0.5' to each side of the equation. 0.5 + -0.5 + 0.625z = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.625z = 2.5 + -0.5 0.625z = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 0.625z = 2 Divide each side by '0.625'. z = 3.2 Simplifying z = 3.2
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