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Simplifying 0.4(2z + 6) + 0.1 = 0.5(2z + -3) Reorder the terms: 0.4(6 + 2z) + 0.1 = 0.5(2z + -3) (6 * 0.4 + 2z * 0.4) + 0.1 = 0.5(2z + -3) (2.4 + 0.8z) + 0.1 = 0.5(2z + -3) Reorder the terms: 2.4 + 0.1 + 0.8z = 0.5(2z + -3) Combine like terms: 2.4 + 0.1 = 2.5 2.5 + 0.8z = 0.5(2z + -3) Reorder the terms: 2.5 + 0.8z = 0.5(-3 + 2z) 2.5 + 0.8z = (-3 * 0.5 + 2z * 0.5) 2.5 + 0.8z = (-1.5 + 1z) Solving 2.5 + 0.8z = -1.5 + 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. 2.5 + 0.8z + -1z = -1.5 + 1z + -1z Combine like terms: 0.8z + -1z = -0.2z 2.5 + -0.2z = -1.5 + 1z + -1z Combine like terms: 1z + -1z = 0 2.5 + -0.2z = -1.5 + 0 2.5 + -0.2z = -1.5 Add '-2.5' to each side of the equation. 2.5 + -2.5 + -0.2z = -1.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -0.2z = -1.5 + -2.5 -0.2z = -1.5 + -2.5 Combine like terms: -1.5 + -2.5 = -4 -0.2z = -4 Divide each side by '-0.2'. z = 20 Simplifying z = 20
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