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Simplifying 0.5(3z + 5) + 0.5 = 0.6(3z + -5) Reorder the terms: 0.5(5 + 3z) + 0.5 = 0.6(3z + -5) (5 * 0.5 + 3z * 0.5) + 0.5 = 0.6(3z + -5) (2.5 + 1.5z) + 0.5 = 0.6(3z + -5) Reorder the terms: 2.5 + 0.5 + 1.5z = 0.6(3z + -5) Combine like terms: 2.5 + 0.5 = 3 3 + 1.5z = 0.6(3z + -5) Reorder the terms: 3 + 1.5z = 0.6(-5 + 3z) 3 + 1.5z = (-5 * 0.6 + 3z * 0.6) 3 + 1.5z = (-3 + 1.8z) Solving 3 + 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. 3 + 1.5z + -1.8z = -3 + 1.8z + -1.8z Combine like terms: 1.5z + -1.8z = -0.3z 3 + -0.3z = -3 + 1.8z + -1.8z Combine like terms: 1.8z + -1.8z = 0.0 3 + -0.3z = -3 + 0.0 3 + -0.3z = -3 Add '-3' to each side of the equation. 3 + -3 + -0.3z = -3 + -3 Combine like terms: 3 + -3 = 0 0 + -0.3z = -3 + -3 -0.3z = -3 + -3 Combine like terms: -3 + -3 = -6 -0.3z = -6 Divide each side by '-0.3'. z = 20 Simplifying z = 20
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