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Simplifying 0.5z + 2 + 3z + 0.75 = 5z + 2 Reorder the terms: 2 + 0.75 + 0.5z + 3z = 5z + 2 Combine like terms: 2 + 0.75 = 2.75 2.75 + 0.5z + 3z = 5z + 2 Combine like terms: 0.5z + 3z = 3.5z 2.75 + 3.5z = 5z + 2 Reorder the terms: 2.75 + 3.5z = 2 + 5z Solving 2.75 + 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. 2.75 + 3.5z + -5z = 2 + 5z + -5z Combine like terms: 3.5z + -5z = -1.5z 2.75 + -1.5z = 2 + 5z + -5z Combine like terms: 5z + -5z = 0 2.75 + -1.5z = 2 + 0 2.75 + -1.5z = 2 Add '-2.75' to each side of the equation. 2.75 + -2.75 + -1.5z = 2 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -1.5z = 2 + -2.75 -1.5z = 2 + -2.75 Combine like terms: 2 + -2.75 = -0.75 -1.5z = -0.75 Divide each side by '-1.5'. z = 0.5 Simplifying z = 0.5
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