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Simplifying 0.5(10z + 2) + -1(z + 9) = 0 Reorder the terms: 0.5(2 + 10z) + -1(z + 9) = 0 (2 * 0.5 + 10z * 0.5) + -1(z + 9) = 0 (1 + 5z) + -1(z + 9) = 0 Reorder the terms: 1 + 5z + -1(9 + z) = 0 1 + 5z + (9 * -1 + z * -1) = 0 1 + 5z + (-9 + -1z) = 0 Reorder the terms: 1 + -9 + 5z + -1z = 0 Combine like terms: 1 + -9 = -8 -8 + 5z + -1z = 0 Combine like terms: 5z + -1z = 4z -8 + 4z = 0 Solving -8 + 4z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 4z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4z = 0 + 8 4z = 0 + 8 Combine like terms: 0 + 8 = 8 4z = 8 Divide each side by '4'. z = 2 Simplifying z = 2
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