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Simplifying 0.3(3z + 7) + 18.9 = 0.5(3z + -6) Reorder the terms: 0.3(7 + 3z) + 18.9 = 0.5(3z + -6) (7 * 0.3 + 3z * 0.3) + 18.9 = 0.5(3z + -6) (2.1 + 0.9z) + 18.9 = 0.5(3z + -6) Reorder the terms: 2.1 + 18.9 + 0.9z = 0.5(3z + -6) Combine like terms: 2.1 + 18.9 = 21 21 + 0.9z = 0.5(3z + -6) Reorder the terms: 21 + 0.9z = 0.5(-6 + 3z) 21 + 0.9z = (-6 * 0.5 + 3z * 0.5) 21 + 0.9z = (-3 + 1.5z) Solving 21 + 0.9z = -3 + 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. 21 + 0.9z + -1.5z = -3 + 1.5z + -1.5z Combine like terms: 0.9z + -1.5z = -0.6z 21 + -0.6z = -3 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 21 + -0.6z = -3 + 0.0 21 + -0.6z = -3 Add '-21' to each side of the equation. 21 + -21 + -0.6z = -3 + -21 Combine like terms: 21 + -21 = 0 0 + -0.6z = -3 + -21 -0.6z = -3 + -21 Combine like terms: -3 + -21 = -24 -0.6z = -24 Divide each side by '-0.6'. z = 40 Simplifying z = 40
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