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Simplifying 0.25(4z + 1) = -0.50(2z + -1) Reorder the terms: 0.25(1 + 4z) = -0.50(2z + -1) (1 * 0.25 + 4z * 0.25) = -0.50(2z + -1) (0.25 + 1z) = -0.50(2z + -1) Reorder the terms: 0.25 + 1z = -0.50(-1 + 2z) 0.25 + 1z = (-1 * -0.50 + 2z * -0.50) 0.25 + 1z = (0.5 + -1z) Solving 0.25 + 1z = 0.5 + -1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add 'z' to each side of the equation. 0.25 + 1z + z = 0.5 + -1z + z Combine like terms: 1z + z = 2z 0.25 + 2z = 0.5 + -1z + z Combine like terms: -1z + z = 0 0.25 + 2z = 0.5 + 0 0.25 + 2z = 0.5 Add '-0.25' to each side of the equation. 0.25 + -0.25 + 2z = 0.5 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2z = 0.5 + -0.25 2z = 0.5 + -0.25 Combine like terms: 0.5 + -0.25 = 0.25 2z = 0.25 Divide each side by '2'. z = 0.125 Simplifying z = 0.125
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