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Simplifying 4(5z + -1) + -5(z + 4) = 5(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 4) = 5(z + 1) (-1 * 4 + 5z * 4) + -5(z + 4) = 5(z + 1) (-4 + 20z) + -5(z + 4) = 5(z + 1) Reorder the terms: -4 + 20z + -5(4 + z) = 5(z + 1) -4 + 20z + (4 * -5 + z * -5) = 5(z + 1) -4 + 20z + (-20 + -5z) = 5(z + 1) Reorder the terms: -4 + -20 + 20z + -5z = 5(z + 1) Combine like terms: -4 + -20 = -24 -24 + 20z + -5z = 5(z + 1) Combine like terms: 20z + -5z = 15z -24 + 15z = 5(z + 1) Reorder the terms: -24 + 15z = 5(1 + z) -24 + 15z = (1 * 5 + z * 5) -24 + 15z = (5 + 5z) Solving -24 + 15z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -24 + 15z + -5z = 5 + 5z + -5z Combine like terms: 15z + -5z = 10z -24 + 10z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -24 + 10z = 5 + 0 -24 + 10z = 5 Add '24' to each side of the equation. -24 + 24 + 10z = 5 + 24 Combine like terms: -24 + 24 = 0 0 + 10z = 5 + 24 10z = 5 + 24 Combine like terms: 5 + 24 = 29 10z = 29 Divide each side by '10'. z = 2.9 Simplifying z = 2.9
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