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Simplifying 4(5z + -1) + -5(z + 1) = 4(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 1) = 4(z + 1) (-1 * 4 + 5z * 4) + -5(z + 1) = 4(z + 1) (-4 + 20z) + -5(z + 1) = 4(z + 1) Reorder the terms: -4 + 20z + -5(1 + z) = 4(z + 1) -4 + 20z + (1 * -5 + z * -5) = 4(z + 1) -4 + 20z + (-5 + -5z) = 4(z + 1) Reorder the terms: -4 + -5 + 20z + -5z = 4(z + 1) Combine like terms: -4 + -5 = -9 -9 + 20z + -5z = 4(z + 1) Combine like terms: 20z + -5z = 15z -9 + 15z = 4(z + 1) Reorder the terms: -9 + 15z = 4(1 + z) -9 + 15z = (1 * 4 + z * 4) -9 + 15z = (4 + 4z) Solving -9 + 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. -9 + 15z + -4z = 4 + 4z + -4z Combine like terms: 15z + -4z = 11z -9 + 11z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -9 + 11z = 4 + 0 -9 + 11z = 4 Add '9' to each side of the equation. -9 + 9 + 11z = 4 + 9 Combine like terms: -9 + 9 = 0 0 + 11z = 4 + 9 11z = 4 + 9 Combine like terms: 4 + 9 = 13 11z = 13 Divide each side by '11'. z = 1.181818182 Simplifying z = 1.181818182
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