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Simplifying 0.3(3z + 5) + 4.5 = 0.5(3z + -5) Reorder the terms: 0.3(5 + 3z) + 4.5 = 0.5(3z + -5) (5 * 0.3 + 3z * 0.3) + 4.5 = 0.5(3z + -5) (1.5 + 0.9z) + 4.5 = 0.5(3z + -5) Reorder the terms: 1.5 + 4.5 + 0.9z = 0.5(3z + -5) Combine like terms: 1.5 + 4.5 = 6 6 + 0.9z = 0.5(3z + -5) Reorder the terms: 6 + 0.9z = 0.5(-5 + 3z) 6 + 0.9z = (-5 * 0.5 + 3z * 0.5) 6 + 0.9z = (-2.5 + 1.5z) Solving 6 + 0.9z = -2.5 + 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. 6 + 0.9z + -1.5z = -2.5 + 1.5z + -1.5z Combine like terms: 0.9z + -1.5z = -0.6z 6 + -0.6z = -2.5 + 1.5z + -1.5z Combine like terms: 1.5z + -1.5z = 0.0 6 + -0.6z = -2.5 + 0.0 6 + -0.6z = -2.5 Add '-6' to each side of the equation. 6 + -6 + -0.6z = -2.5 + -6 Combine like terms: 6 + -6 = 0 0 + -0.6z = -2.5 + -6 -0.6z = -2.5 + -6 Combine like terms: -2.5 + -6 = -8.5 -0.6z = -8.5 Divide each side by '-0.6'. z = 14.16666667 Simplifying z = 14.16666667
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