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Simplifying 0.5z + 2 + 3z + 1.5 = 5z + 2 Reorder the terms: 2 + 1.5 + 0.5z + 3z = 5z + 2 Combine like terms: 2 + 1.5 = 3.5 3.5 + 0.5z + 3z = 5z + 2 Combine like terms: 0.5z + 3z = 3.5z 3.5 + 3.5z = 5z + 2 Reorder the terms: 3.5 + 3.5z = 2 + 5z Solving 3.5 + 3.5z = 2 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. 3.5 + 3.5z + -5z = 2 + 5z + -5z Combine like terms: 3.5z + -5z = -1.5z 3.5 + -1.5z = 2 + 5z + -5z Combine like terms: 5z + -5z = 0 3.5 + -1.5z = 2 + 0 3.5 + -1.5z = 2 Add '-3.5' to each side of the equation. 3.5 + -3.5 + -1.5z = 2 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -1.5z = 2 + -3.5 -1.5z = 2 + -3.5 Combine like terms: 2 + -3.5 = -1.5 -1.5z = -1.5 Divide each side by '-1.5'. z = 1 Simplifying z = 1
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