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Simplifying 0.4(2z + 7) + 2.2 = 0.5(2z + -6) Reorder the terms: 0.4(7 + 2z) + 2.2 = 0.5(2z + -6) (7 * 0.4 + 2z * 0.4) + 2.2 = 0.5(2z + -6) (2.8 + 0.8z) + 2.2 = 0.5(2z + -6) Reorder the terms: 2.8 + 2.2 + 0.8z = 0.5(2z + -6) Combine like terms: 2.8 + 2.2 = 5 5 + 0.8z = 0.5(2z + -6) Reorder the terms: 5 + 0.8z = 0.5(-6 + 2z) 5 + 0.8z = (-6 * 0.5 + 2z * 0.5) 5 + 0.8z = (-3 + 1z) Solving 5 + 0.8z = -3 + 1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. 5 + 0.8z + -1z = -3 + 1z + -1z Combine like terms: 0.8z + -1z = -0.2z 5 + -0.2z = -3 + 1z + -1z Combine like terms: 1z + -1z = 0 5 + -0.2z = -3 + 0 5 + -0.2z = -3 Add '-5' to each side of the equation. 5 + -5 + -0.2z = -3 + -5 Combine like terms: 5 + -5 = 0 0 + -0.2z = -3 + -5 -0.2z = -3 + -5 Combine like terms: -3 + -5 = -8 -0.2z = -8 Divide each side by '-0.2'. z = 40 Simplifying z = 40
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