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Simplifying 5(4z + -1) + -5(z + 8) = 4(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 8) = 4(z + 1) (-1 * 5 + 4z * 5) + -5(z + 8) = 4(z + 1) (-5 + 20z) + -5(z + 8) = 4(z + 1) Reorder the terms: -5 + 20z + -5(8 + z) = 4(z + 1) -5 + 20z + (8 * -5 + z * -5) = 4(z + 1) -5 + 20z + (-40 + -5z) = 4(z + 1) Reorder the terms: -5 + -40 + 20z + -5z = 4(z + 1) Combine like terms: -5 + -40 = -45 -45 + 20z + -5z = 4(z + 1) Combine like terms: 20z + -5z = 15z -45 + 15z = 4(z + 1) Reorder the terms: -45 + 15z = 4(1 + z) -45 + 15z = (1 * 4 + z * 4) -45 + 15z = (4 + 4z) Solving -45 + 15z = 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. -45 + 15z + -4z = 4 + 4z + -4z Combine like terms: 15z + -4z = 11z -45 + 11z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -45 + 11z = 4 + 0 -45 + 11z = 4 Add '45' to each side of the equation. -45 + 45 + 11z = 4 + 45 Combine like terms: -45 + 45 = 0 0 + 11z = 4 + 45 11z = 4 + 45 Combine like terms: 4 + 45 = 49 11z = 49 Divide each side by '11'. z = 4.454545455 Simplifying z = 4.454545455
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