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Simplifying 0.02(800z + 50) = -500 + -24z Reorder the terms: 0.02(50 + 800z) = -500 + -24z (50 * 0.02 + 800z * 0.02) = -500 + -24z (1 + 16z) = -500 + -24z Solving 1 + 16z = -500 + -24z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '24z' to each side of the equation. 1 + 16z + 24z = -500 + -24z + 24z Combine like terms: 16z + 24z = 40z 1 + 40z = -500 + -24z + 24z Combine like terms: -24z + 24z = 0 1 + 40z = -500 + 0 1 + 40z = -500 Add '-1' to each side of the equation. 1 + -1 + 40z = -500 + -1 Combine like terms: 1 + -1 = 0 0 + 40z = -500 + -1 40z = -500 + -1 Combine like terms: -500 + -1 = -501 40z = -501 Divide each side by '40'. z = -12.525 Simplifying z = -12.525
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