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Simplifying 5(3z + -1) + -4(z + 7) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -4(z + 7) = 8(z + 1) (-1 * 5 + 3z * 5) + -4(z + 7) = 8(z + 1) (-5 + 15z) + -4(z + 7) = 8(z + 1) Reorder the terms: -5 + 15z + -4(7 + z) = 8(z + 1) -5 + 15z + (7 * -4 + z * -4) = 8(z + 1) -5 + 15z + (-28 + -4z) = 8(z + 1) Reorder the terms: -5 + -28 + 15z + -4z = 8(z + 1) Combine like terms: -5 + -28 = -33 -33 + 15z + -4z = 8(z + 1) Combine like terms: 15z + -4z = 11z -33 + 11z = 8(z + 1) Reorder the terms: -33 + 11z = 8(1 + z) -33 + 11z = (1 * 8 + z * 8) -33 + 11z = (8 + 8z) Solving -33 + 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. -33 + 11z + -8z = 8 + 8z + -8z Combine like terms: 11z + -8z = 3z -33 + 3z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -33 + 3z = 8 + 0 -33 + 3z = 8 Add '33' to each side of the equation. -33 + 33 + 3z = 8 + 33 Combine like terms: -33 + 33 = 0 0 + 3z = 8 + 33 3z = 8 + 33 Combine like terms: 8 + 33 = 41 3z = 41 Divide each side by '3'. z = 13.66666667 Simplifying z = 13.66666667
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