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Simplifying 0.4(4z + 6) + 3.1 = 0.5(4z + -5) Reorder the terms: 0.4(6 + 4z) + 3.1 = 0.5(4z + -5) (6 * 0.4 + 4z * 0.4) + 3.1 = 0.5(4z + -5) (2.4 + 1.6z) + 3.1 = 0.5(4z + -5) Reorder the terms: 2.4 + 3.1 + 1.6z = 0.5(4z + -5) Combine like terms: 2.4 + 3.1 = 5.5 5.5 + 1.6z = 0.5(4z + -5) Reorder the terms: 5.5 + 1.6z = 0.5(-5 + 4z) 5.5 + 1.6z = (-5 * 0.5 + 4z * 0.5) 5.5 + 1.6z = (-2.5 + 2z) Solving 5.5 + 1.6z = -2.5 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. 5.5 + 1.6z + -2z = -2.5 + 2z + -2z Combine like terms: 1.6z + -2z = -0.4z 5.5 + -0.4z = -2.5 + 2z + -2z Combine like terms: 2z + -2z = 0 5.5 + -0.4z = -2.5 + 0 5.5 + -0.4z = -2.5 Add '-5.5' to each side of the equation. 5.5 + -5.5 + -0.4z = -2.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -0.4z = -2.5 + -5.5 -0.4z = -2.5 + -5.5 Combine like terms: -2.5 + -5.5 = -8 -0.4z = -8 Divide each side by '-0.4'. z = 20 Simplifying z = 20
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