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Simplifying 0.5(3z + 7) + 5.5 = 0.6(3z + -5) Reorder the terms: 0.5(7 + 3z) + 5.5 = 0.6(3z + -5) (7 * 0.5 + 3z * 0.5) + 5.5 = 0.6(3z + -5) (3.5 + 1.5z) + 5.5 = 0.6(3z + -5) Reorder the terms: 3.5 + 5.5 + 1.5z = 0.6(3z + -5) Combine like terms: 3.5 + 5.5 = 9 9 + 1.5z = 0.6(3z + -5) Reorder the terms: 9 + 1.5z = 0.6(-5 + 3z) 9 + 1.5z = (-5 * 0.6 + 3z * 0.6) 9 + 1.5z = (-3 + 1.8z) Solving 9 + 1.5z = -3 + 1.8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.8z' to each side of the equation. 9 + 1.5z + -1.8z = -3 + 1.8z + -1.8z Combine like terms: 1.5z + -1.8z = -0.3z 9 + -0.3z = -3 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 9 + -0.3z = -3 + 0.0 9 + -0.3z = -3 Add '-9' to each side of the equation. 9 + -9 + -0.3z = -3 + -9 Combine like terms: 9 + -9 = 0 0 + -0.3z = -3 + -9 -0.3z = -3 + -9 Combine like terms: -3 + -9 = -12 -0.3z = -12 Divide each side by '-0.3'. z = 40 Simplifying z = 40
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