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Simplifying 0.4(2z + 6) + 0.1 = 0.5(6z + -8) Reorder the terms: 0.4(6 + 2z) + 0.1 = 0.5(6z + -8) (6 * 0.4 + 2z * 0.4) + 0.1 = 0.5(6z + -8) (2.4 + 0.8z) + 0.1 = 0.5(6z + -8) Reorder the terms: 2.4 + 0.1 + 0.8z = 0.5(6z + -8) Combine like terms: 2.4 + 0.1 = 2.5 2.5 + 0.8z = 0.5(6z + -8) Reorder the terms: 2.5 + 0.8z = 0.5(-8 + 6z) 2.5 + 0.8z = (-8 * 0.5 + 6z * 0.5) 2.5 + 0.8z = (-4 + 3z) Solving 2.5 + 0.8z = -4 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. 2.5 + 0.8z + -3z = -4 + 3z + -3z Combine like terms: 0.8z + -3z = -2.2z 2.5 + -2.2z = -4 + 3z + -3z Combine like terms: 3z + -3z = 0 2.5 + -2.2z = -4 + 0 2.5 + -2.2z = -4 Add '-2.5' to each side of the equation. 2.5 + -2.5 + -2.2z = -4 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2.2z = -4 + -2.5 -2.2z = -4 + -2.5 Combine like terms: -4 + -2.5 = -6.5 -2.2z = -6.5 Divide each side by '-2.2'. z = 2.954545455 Simplifying z = 2.954545455
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