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Simplifying 5(4z + -1) + -2(z + 8) = 11(z + 1) Reorder the terms: 5(-1 + 4z) + -2(z + 8) = 11(z + 1) (-1 * 5 + 4z * 5) + -2(z + 8) = 11(z + 1) (-5 + 20z) + -2(z + 8) = 11(z + 1) Reorder the terms: -5 + 20z + -2(8 + z) = 11(z + 1) -5 + 20z + (8 * -2 + z * -2) = 11(z + 1) -5 + 20z + (-16 + -2z) = 11(z + 1) Reorder the terms: -5 + -16 + 20z + -2z = 11(z + 1) Combine like terms: -5 + -16 = -21 -21 + 20z + -2z = 11(z + 1) Combine like terms: 20z + -2z = 18z -21 + 18z = 11(z + 1) Reorder the terms: -21 + 18z = 11(1 + z) -21 + 18z = (1 * 11 + z * 11) -21 + 18z = (11 + 11z) Solving -21 + 18z = 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. -21 + 18z + -11z = 11 + 11z + -11z Combine like terms: 18z + -11z = 7z -21 + 7z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -21 + 7z = 11 + 0 -21 + 7z = 11 Add '21' to each side of the equation. -21 + 21 + 7z = 11 + 21 Combine like terms: -21 + 21 = 0 0 + 7z = 11 + 21 7z = 11 + 21 Combine like terms: 11 + 21 = 32 7z = 32 Divide each side by '7'. z = 4.571428571 Simplifying z = 4.571428571
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