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Simplifying 5(4z + -1) + -4(z + 4) = 4(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 4) = 4(z + 1) (-1 * 5 + 4z * 5) + -4(z + 4) = 4(z + 1) (-5 + 20z) + -4(z + 4) = 4(z + 1) Reorder the terms: -5 + 20z + -4(4 + z) = 4(z + 1) -5 + 20z + (4 * -4 + z * -4) = 4(z + 1) -5 + 20z + (-16 + -4z) = 4(z + 1) Reorder the terms: -5 + -16 + 20z + -4z = 4(z + 1) Combine like terms: -5 + -16 = -21 -21 + 20z + -4z = 4(z + 1) Combine like terms: 20z + -4z = 16z -21 + 16z = 4(z + 1) Reorder the terms: -21 + 16z = 4(1 + z) -21 + 16z = (1 * 4 + z * 4) -21 + 16z = (4 + 4z) Solving -21 + 16z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -21 + 16z + -4z = 4 + 4z + -4z Combine like terms: 16z + -4z = 12z -21 + 12z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -21 + 12z = 4 + 0 -21 + 12z = 4 Add '21' to each side of the equation. -21 + 21 + 12z = 4 + 21 Combine like terms: -21 + 21 = 0 0 + 12z = 4 + 21 12z = 4 + 21 Combine like terms: 4 + 21 = 25 12z = 25 Divide each side by '12'. z = 2.083333333 Simplifying z = 2.083333333
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