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Simplifying 24.5 = -9.5 + 7.5(z + 5.5) Reorder the terms: 24.5 = -9.5 + 7.5(5.5 + z) 24.5 = -9.5 + (5.5 * 7.5 + z * 7.5) 24.5 = -9.5 + (41.25 + 7.5z) Combine like terms: -9.5 + 41.25 = 31.75 24.5 = 31.75 + 7.5z Solving 24.5 = 31.75 + 7.5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7.5z' to each side of the equation. 24.5 + -7.5z = 31.75 + 7.5z + -7.5z Combine like terms: 7.5z + -7.5z = 0.0 24.5 + -7.5z = 31.75 + 0.0 24.5 + -7.5z = 31.75 Add '-24.5' to each side of the equation. 24.5 + -24.5 + -7.5z = 31.75 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + -7.5z = 31.75 + -24.5 -7.5z = 31.75 + -24.5 Combine like terms: 31.75 + -24.5 = 7.25 -7.5z = 7.25 Divide each side by '-7.5'. z = -0.9666666667 Simplifying z = -0.9666666667
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