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Simplifying 5(4z + -1) + -4(z + 1) = 2(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 1) = 2(z + 1) (-1 * 5 + 4z * 5) + -4(z + 1) = 2(z + 1) (-5 + 20z) + -4(z + 1) = 2(z + 1) Reorder the terms: -5 + 20z + -4(1 + z) = 2(z + 1) -5 + 20z + (1 * -4 + z * -4) = 2(z + 1) -5 + 20z + (-4 + -4z) = 2(z + 1) Reorder the terms: -5 + -4 + 20z + -4z = 2(z + 1) Combine like terms: -5 + -4 = -9 -9 + 20z + -4z = 2(z + 1) Combine like terms: 20z + -4z = 16z -9 + 16z = 2(z + 1) Reorder the terms: -9 + 16z = 2(1 + z) -9 + 16z = (1 * 2 + z * 2) -9 + 16z = (2 + 2z) Solving -9 + 16z = 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. -9 + 16z + -2z = 2 + 2z + -2z Combine like terms: 16z + -2z = 14z -9 + 14z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -9 + 14z = 2 + 0 -9 + 14z = 2 Add '9' to each side of the equation. -9 + 9 + 14z = 2 + 9 Combine like terms: -9 + 9 = 0 0 + 14z = 2 + 9 14z = 2 + 9 Combine like terms: 2 + 9 = 11 14z = 11 Divide each side by '14'. z = 0.7857142857 Simplifying z = 0.7857142857
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