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Simplifying 0.4(3z + 6) + 7.6 = 0.5(3z + -4) Reorder the terms: 0.4(6 + 3z) + 7.6 = 0.5(3z + -4) (6 * 0.4 + 3z * 0.4) + 7.6 = 0.5(3z + -4) (2.4 + 1.2z) + 7.6 = 0.5(3z + -4) Reorder the terms: 2.4 + 7.6 + 1.2z = 0.5(3z + -4) Combine like terms: 2.4 + 7.6 = 10 10 + 1.2z = 0.5(3z + -4) Reorder the terms: 10 + 1.2z = 0.5(-4 + 3z) 10 + 1.2z = (-4 * 0.5 + 3z * 0.5) 10 + 1.2z = (-2 + 1.5z) Solving 10 + 1.2z = -2 + 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. 10 + 1.2z + -1.5z = -2 + 1.5z + -1.5z Combine like terms: 1.2z + -1.5z = -0.3z 10 + -0.3z = -2 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 10 + -0.3z = -2 + 0.0 10 + -0.3z = -2 Add '-10' to each side of the equation. 10 + -10 + -0.3z = -2 + -10 Combine like terms: 10 + -10 = 0 0 + -0.3z = -2 + -10 -0.3z = -2 + -10 Combine like terms: -2 + -10 = -12 -0.3z = -12 Divide each side by '-0.3'. z = 40 Simplifying z = 40
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