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Simplifying 0.5(z + 5) + 3 = 0.25(7z + -11) + -8 Reorder the terms: 0.5(5 + z) + 3 = 0.25(7z + -11) + -8 (5 * 0.5 + z * 0.5) + 3 = 0.25(7z + -11) + -8 (2.5 + 0.5z) + 3 = 0.25(7z + -11) + -8 Reorder the terms: 2.5 + 3 + 0.5z = 0.25(7z + -11) + -8 Combine like terms: 2.5 + 3 = 5.5 5.5 + 0.5z = 0.25(7z + -11) + -8 Reorder the terms: 5.5 + 0.5z = 0.25(-11 + 7z) + -8 5.5 + 0.5z = (-11 * 0.25 + 7z * 0.25) + -8 5.5 + 0.5z = (-2.75 + 1.75z) + -8 Reorder the terms: 5.5 + 0.5z = -2.75 + -8 + 1.75z Combine like terms: -2.75 + -8 = -10.75 5.5 + 0.5z = -10.75 + 1.75z Solving 5.5 + 0.5z = -10.75 + 1.75z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.75z' to each side of the equation. 5.5 + 0.5z + -1.75z = -10.75 + 1.75z + -1.75z Combine like terms: 0.5z + -1.75z = -1.25z 5.5 + -1.25z = -10.75 + 1.75z + -1.75z Combine like terms: 1.75z + -1.75z = 0.00 5.5 + -1.25z = -10.75 + 0.00 5.5 + -1.25z = -10.75 Add '-5.5' to each side of the equation. 5.5 + -5.5 + -1.25z = -10.75 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -1.25z = -10.75 + -5.5 -1.25z = -10.75 + -5.5 Combine like terms: -10.75 + -5.5 = -16.25 -1.25z = -16.25 Divide each side by '-1.25'. z = 13 Simplifying z = 13
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