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Simplifying 0.4(3z + 6) + 7.1 = 0.5(3z + -5) Reorder the terms: 0.4(6 + 3z) + 7.1 = 0.5(3z + -5) (6 * 0.4 + 3z * 0.4) + 7.1 = 0.5(3z + -5) (2.4 + 1.2z) + 7.1 = 0.5(3z + -5) Reorder the terms: 2.4 + 7.1 + 1.2z = 0.5(3z + -5) Combine like terms: 2.4 + 7.1 = 9.5 9.5 + 1.2z = 0.5(3z + -5) Reorder the terms: 9.5 + 1.2z = 0.5(-5 + 3z) 9.5 + 1.2z = (-5 * 0.5 + 3z * 0.5) 9.5 + 1.2z = (-2.5 + 1.5z) Solving 9.5 + 1.2z = -2.5 + 1.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.5z' to each side of the equation. 9.5 + 1.2z + -1.5z = -2.5 + 1.5z + -1.5z Combine like terms: 1.2z + -1.5z = -0.3z 9.5 + -0.3z = -2.5 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 9.5 + -0.3z = -2.5 + 0.0 9.5 + -0.3z = -2.5 Add '-9.5' to each side of the equation. 9.5 + -9.5 + -0.3z = -2.5 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -0.3z = -2.5 + -9.5 -0.3z = -2.5 + -9.5 Combine like terms: -2.5 + -9.5 = -12 -0.3z = -12 Divide each side by '-0.3'. z = 40 Simplifying z = 40
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