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Simplifying 5(4z + -1) + -4(z + 1) = 14(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 1) = 14(z + 1) (-1 * 5 + 4z * 5) + -4(z + 1) = 14(z + 1) (-5 + 20z) + -4(z + 1) = 14(z + 1) Reorder the terms: -5 + 20z + -4(1 + z) = 14(z + 1) -5 + 20z + (1 * -4 + z * -4) = 14(z + 1) -5 + 20z + (-4 + -4z) = 14(z + 1) Reorder the terms: -5 + -4 + 20z + -4z = 14(z + 1) Combine like terms: -5 + -4 = -9 -9 + 20z + -4z = 14(z + 1) Combine like terms: 20z + -4z = 16z -9 + 16z = 14(z + 1) Reorder the terms: -9 + 16z = 14(1 + z) -9 + 16z = (1 * 14 + z * 14) -9 + 16z = (14 + 14z) Solving -9 + 16z = 14 + 14z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14z' to each side of the equation. -9 + 16z + -14z = 14 + 14z + -14z Combine like terms: 16z + -14z = 2z -9 + 2z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -9 + 2z = 14 + 0 -9 + 2z = 14 Add '9' to each side of the equation. -9 + 9 + 2z = 14 + 9 Combine like terms: -9 + 9 = 0 0 + 2z = 14 + 9 2z = 14 + 9 Combine like terms: 14 + 9 = 23 2z = 23 Divide each side by '2'. z = 11.5 Simplifying z = 11.5
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