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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 for easier multiplication: 3.5 + 3.5z = 5 * 2z Multiply 5 * 2 3.5 + 3.5z = 10z Solving 3.5 + 3.5z = 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. 3.5 + 3.5z + -10z = 10z + -10z Combine like terms: 3.5z + -10z = -6.5z 3.5 + -6.5z = 10z + -10z Combine like terms: 10z + -10z = 0 3.5 + -6.5z = 0 Add '-3.5' to each side of the equation. 3.5 + -3.5 + -6.5z = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -6.5z = 0 + -3.5 -6.5z = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -6.5z = -3.5 Divide each side by '-6.5'. z = 0.5384615385 Simplifying z = 0.5384615385
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