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Simplifying 5(4z + -1) + -5(z + 7) = 12(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 7) = 12(z + 1) (-1 * 5 + 4z * 5) + -5(z + 7) = 12(z + 1) (-5 + 20z) + -5(z + 7) = 12(z + 1) Reorder the terms: -5 + 20z + -5(7 + z) = 12(z + 1) -5 + 20z + (7 * -5 + z * -5) = 12(z + 1) -5 + 20z + (-35 + -5z) = 12(z + 1) Reorder the terms: -5 + -35 + 20z + -5z = 12(z + 1) Combine like terms: -5 + -35 = -40 -40 + 20z + -5z = 12(z + 1) Combine like terms: 20z + -5z = 15z -40 + 15z = 12(z + 1) Reorder the terms: -40 + 15z = 12(1 + z) -40 + 15z = (1 * 12 + z * 12) -40 + 15z = (12 + 12z) Solving -40 + 15z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -40 + 15z + -12z = 12 + 12z + -12z Combine like terms: 15z + -12z = 3z -40 + 3z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -40 + 3z = 12 + 0 -40 + 3z = 12 Add '40' to each side of the equation. -40 + 40 + 3z = 12 + 40 Combine like terms: -40 + 40 = 0 0 + 3z = 12 + 40 3z = 12 + 40 Combine like terms: 12 + 40 = 52 3z = 52 Divide each side by '3'. z = 17.33333333 Simplifying z = 17.33333333
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