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Simplifying 0.3(3z + 7) + 12.9 = 0.6(3z + -5) Reorder the terms: 0.3(7 + 3z) + 12.9 = 0.6(3z + -5) (7 * 0.3 + 3z * 0.3) + 12.9 = 0.6(3z + -5) (2.1 + 0.9z) + 12.9 = 0.6(3z + -5) Reorder the terms: 2.1 + 12.9 + 0.9z = 0.6(3z + -5) Combine like terms: 2.1 + 12.9 = 15 15 + 0.9z = 0.6(3z + -5) Reorder the terms: 15 + 0.9z = 0.6(-5 + 3z) 15 + 0.9z = (-5 * 0.6 + 3z * 0.6) 15 + 0.9z = (-3 + 1.8z) Solving 15 + 0.9z = -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. 15 + 0.9z + -1.8z = -3 + 1.8z + -1.8z Combine like terms: 0.9z + -1.8z = -0.9z 15 + -0.9z = -3 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 15 + -0.9z = -3 + 0.0 15 + -0.9z = -3 Add '-15' to each side of the equation. 15 + -15 + -0.9z = -3 + -15 Combine like terms: 15 + -15 = 0 0 + -0.9z = -3 + -15 -0.9z = -3 + -15 Combine like terms: -3 + -15 = -18 -0.9z = -18 Divide each side by '-0.9'. z = 20 Simplifying z = 20
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