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Simplifying 8(z + 2) + 13z = 11(z + 1) + 2z Reorder the terms: 8(2 + z) + 13z = 11(z + 1) + 2z (2 * 8 + z * 8) + 13z = 11(z + 1) + 2z (16 + 8z) + 13z = 11(z + 1) + 2z Combine like terms: 8z + 13z = 21z 16 + 21z = 11(z + 1) + 2z Reorder the terms: 16 + 21z = 11(1 + z) + 2z 16 + 21z = (1 * 11 + z * 11) + 2z 16 + 21z = (11 + 11z) + 2z Combine like terms: 11z + 2z = 13z 16 + 21z = 11 + 13z Solving 16 + 21z = 11 + 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. 16 + 21z + -13z = 11 + 13z + -13z Combine like terms: 21z + -13z = 8z 16 + 8z = 11 + 13z + -13z Combine like terms: 13z + -13z = 0 16 + 8z = 11 + 0 16 + 8z = 11 Add '-16' to each side of the equation. 16 + -16 + 8z = 11 + -16 Combine like terms: 16 + -16 = 0 0 + 8z = 11 + -16 8z = 11 + -16 Combine like terms: 11 + -16 = -5 8z = -5 Divide each side by '8'. z = -0.625 Simplifying z = -0.625
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