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Simplifying 5(4z + -1) + -5(z + 7) = 2(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 7) = 2(z + 1) (-1 * 5 + 4z * 5) + -5(z + 7) = 2(z + 1) (-5 + 20z) + -5(z + 7) = 2(z + 1) Reorder the terms: -5 + 20z + -5(7 + z) = 2(z + 1) -5 + 20z + (7 * -5 + z * -5) = 2(z + 1) -5 + 20z + (-35 + -5z) = 2(z + 1) Reorder the terms: -5 + -35 + 20z + -5z = 2(z + 1) Combine like terms: -5 + -35 = -40 -40 + 20z + -5z = 2(z + 1) Combine like terms: 20z + -5z = 15z -40 + 15z = 2(z + 1) Reorder the terms: -40 + 15z = 2(1 + z) -40 + 15z = (1 * 2 + z * 2) -40 + 15z = (2 + 2z) Solving -40 + 15z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -40 + 15z + -2z = 2 + 2z + -2z Combine like terms: 15z + -2z = 13z -40 + 13z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -40 + 13z = 2 + 0 -40 + 13z = 2 Add '40' to each side of the equation. -40 + 40 + 13z = 2 + 40 Combine like terms: -40 + 40 = 0 0 + 13z = 2 + 40 13z = 2 + 40 Combine like terms: 2 + 40 = 42 13z = 42 Divide each side by '13'. z = 3.230769231 Simplifying z = 3.230769231
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