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Simplifying 0.3(3z + 6) + 20.2 = 0.5(3z + -4) Reorder the terms: 0.3(6 + 3z) + 20.2 = 0.5(3z + -4) (6 * 0.3 + 3z * 0.3) + 20.2 = 0.5(3z + -4) (1.8 + 0.9z) + 20.2 = 0.5(3z + -4) Reorder the terms: 1.8 + 20.2 + 0.9z = 0.5(3z + -4) Combine like terms: 1.8 + 20.2 = 22 22 + 0.9z = 0.5(3z + -4) Reorder the terms: 22 + 0.9z = 0.5(-4 + 3z) 22 + 0.9z = (-4 * 0.5 + 3z * 0.5) 22 + 0.9z = (-2 + 1.5z) Solving 22 + 0.9z = -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. 22 + 0.9z + -1.5z = -2 + 1.5z + -1.5z Combine like terms: 0.9z + -1.5z = -0.6z 22 + -0.6z = -2 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 22 + -0.6z = -2 + 0.0 22 + -0.6z = -2 Add '-22' to each side of the equation. 22 + -22 + -0.6z = -2 + -22 Combine like terms: 22 + -22 = 0 0 + -0.6z = -2 + -22 -0.6z = -2 + -22 Combine like terms: -2 + -22 = -24 -0.6z = -24 Divide each side by '-0.6'. z = 40 Simplifying z = 40
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