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Simplifying 5(4z + -1) + -5(z + 4) = 2(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 4) = 2(z + 1) (-1 * 5 + 4z * 5) + -5(z + 4) = 2(z + 1) (-5 + 20z) + -5(z + 4) = 2(z + 1) Reorder the terms: -5 + 20z + -5(4 + z) = 2(z + 1) -5 + 20z + (4 * -5 + z * -5) = 2(z + 1) -5 + 20z + (-20 + -5z) = 2(z + 1) Reorder the terms: -5 + -20 + 20z + -5z = 2(z + 1) Combine like terms: -5 + -20 = -25 -25 + 20z + -5z = 2(z + 1) Combine like terms: 20z + -5z = 15z -25 + 15z = 2(z + 1) Reorder the terms: -25 + 15z = 2(1 + z) -25 + 15z = (1 * 2 + z * 2) -25 + 15z = (2 + 2z) Solving -25 + 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. -25 + 15z + -2z = 2 + 2z + -2z Combine like terms: 15z + -2z = 13z -25 + 13z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -25 + 13z = 2 + 0 -25 + 13z = 2 Add '25' to each side of the equation. -25 + 25 + 13z = 2 + 25 Combine like terms: -25 + 25 = 0 0 + 13z = 2 + 25 13z = 2 + 25 Combine like terms: 2 + 25 = 27 13z = 27 Divide each side by '13'. z = 2.076923077 Simplifying z = 2.076923077
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