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Simplifying 5(4z + -1) + -5(z + 5) = 4(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 5) = 4(z + 1) (-1 * 5 + 4z * 5) + -5(z + 5) = 4(z + 1) (-5 + 20z) + -5(z + 5) = 4(z + 1) Reorder the terms: -5 + 20z + -5(5 + z) = 4(z + 1) -5 + 20z + (5 * -5 + z * -5) = 4(z + 1) -5 + 20z + (-25 + -5z) = 4(z + 1) Reorder the terms: -5 + -25 + 20z + -5z = 4(z + 1) Combine like terms: -5 + -25 = -30 -30 + 20z + -5z = 4(z + 1) Combine like terms: 20z + -5z = 15z -30 + 15z = 4(z + 1) Reorder the terms: -30 + 15z = 4(1 + z) -30 + 15z = (1 * 4 + z * 4) -30 + 15z = (4 + 4z) Solving -30 + 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. -30 + 15z + -4z = 4 + 4z + -4z Combine like terms: 15z + -4z = 11z -30 + 11z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -30 + 11z = 4 + 0 -30 + 11z = 4 Add '30' to each side of the equation. -30 + 30 + 11z = 4 + 30 Combine like terms: -30 + 30 = 0 0 + 11z = 4 + 30 11z = 4 + 30 Combine like terms: 4 + 30 = 34 11z = 34 Divide each side by '11'. z = 3.090909091 Simplifying z = 3.090909091
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