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Simplifying 8(z + 3) + 7(z + 2) = 5z + 6(z + 1) Reorder the terms: 8(3 + z) + 7(z + 2) = 5z + 6(z + 1) (3 * 8 + z * 8) + 7(z + 2) = 5z + 6(z + 1) (24 + 8z) + 7(z + 2) = 5z + 6(z + 1) Reorder the terms: 24 + 8z + 7(2 + z) = 5z + 6(z + 1) 24 + 8z + (2 * 7 + z * 7) = 5z + 6(z + 1) 24 + 8z + (14 + 7z) = 5z + 6(z + 1) Reorder the terms: 24 + 14 + 8z + 7z = 5z + 6(z + 1) Combine like terms: 24 + 14 = 38 38 + 8z + 7z = 5z + 6(z + 1) Combine like terms: 8z + 7z = 15z 38 + 15z = 5z + 6(z + 1) Reorder the terms: 38 + 15z = 5z + 6(1 + z) 38 + 15z = 5z + (1 * 6 + z * 6) 38 + 15z = 5z + (6 + 6z) Reorder the terms: 38 + 15z = 6 + 5z + 6z Combine like terms: 5z + 6z = 11z 38 + 15z = 6 + 11z Solving 38 + 15z = 6 + 11z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11z' to each side of the equation. 38 + 15z + -11z = 6 + 11z + -11z Combine like terms: 15z + -11z = 4z 38 + 4z = 6 + 11z + -11z Combine like terms: 11z + -11z = 0 38 + 4z = 6 + 0 38 + 4z = 6 Add '-38' to each side of the equation. 38 + -38 + 4z = 6 + -38 Combine like terms: 38 + -38 = 0 0 + 4z = 6 + -38 4z = 6 + -38 Combine like terms: 6 + -38 = -32 4z = -32 Divide each side by '4'. z = -8 Simplifying z = -8
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