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Simplifying 6(4z + -1) + -4(z + 8) = 11(z + 1) Reorder the terms: 6(-1 + 4z) + -4(z + 8) = 11(z + 1) (-1 * 6 + 4z * 6) + -4(z + 8) = 11(z + 1) (-6 + 24z) + -4(z + 8) = 11(z + 1) Reorder the terms: -6 + 24z + -4(8 + z) = 11(z + 1) -6 + 24z + (8 * -4 + z * -4) = 11(z + 1) -6 + 24z + (-32 + -4z) = 11(z + 1) Reorder the terms: -6 + -32 + 24z + -4z = 11(z + 1) Combine like terms: -6 + -32 = -38 -38 + 24z + -4z = 11(z + 1) Combine like terms: 24z + -4z = 20z -38 + 20z = 11(z + 1) Reorder the terms: -38 + 20z = 11(1 + z) -38 + 20z = (1 * 11 + z * 11) -38 + 20z = (11 + 11z) Solving -38 + 20z = 11 + 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 + 20z + -11z = 11 + 11z + -11z Combine like terms: 20z + -11z = 9z -38 + 9z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -38 + 9z = 11 + 0 -38 + 9z = 11 Add '38' to each side of the equation. -38 + 38 + 9z = 11 + 38 Combine like terms: -38 + 38 = 0 0 + 9z = 11 + 38 9z = 11 + 38 Combine like terms: 11 + 38 = 49 9z = 49 Divide each side by '9'. z = 5.444444444 Simplifying z = 5.444444444
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