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Simplifying 5(3z + -1) + -4(z + 4) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -4(z + 4) = 8(z + 1) (-1 * 5 + 3z * 5) + -4(z + 4) = 8(z + 1) (-5 + 15z) + -4(z + 4) = 8(z + 1) Reorder the terms: -5 + 15z + -4(4 + z) = 8(z + 1) -5 + 15z + (4 * -4 + z * -4) = 8(z + 1) -5 + 15z + (-16 + -4z) = 8(z + 1) Reorder the terms: -5 + -16 + 15z + -4z = 8(z + 1) Combine like terms: -5 + -16 = -21 -21 + 15z + -4z = 8(z + 1) Combine like terms: 15z + -4z = 11z -21 + 11z = 8(z + 1) Reorder the terms: -21 + 11z = 8(1 + z) -21 + 11z = (1 * 8 + z * 8) -21 + 11z = (8 + 8z) Solving -21 + 11z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -21 + 11z + -8z = 8 + 8z + -8z Combine like terms: 11z + -8z = 3z -21 + 3z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -21 + 3z = 8 + 0 -21 + 3z = 8 Add '21' to each side of the equation. -21 + 21 + 3z = 8 + 21 Combine like terms: -21 + 21 = 0 0 + 3z = 8 + 21 3z = 8 + 21 Combine like terms: 8 + 21 = 29 3z = 29 Divide each side by '3'. z = 9.666666667 Simplifying z = 9.666666667
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