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Simplifying 4(5z + -1) + -4(z + 5) = 3(z + 1) Reorder the terms: 4(-1 + 5z) + -4(z + 5) = 3(z + 1) (-1 * 4 + 5z * 4) + -4(z + 5) = 3(z + 1) (-4 + 20z) + -4(z + 5) = 3(z + 1) Reorder the terms: -4 + 20z + -4(5 + z) = 3(z + 1) -4 + 20z + (5 * -4 + z * -4) = 3(z + 1) -4 + 20z + (-20 + -4z) = 3(z + 1) Reorder the terms: -4 + -20 + 20z + -4z = 3(z + 1) Combine like terms: -4 + -20 = -24 -24 + 20z + -4z = 3(z + 1) Combine like terms: 20z + -4z = 16z -24 + 16z = 3(z + 1) Reorder the terms: -24 + 16z = 3(1 + z) -24 + 16z = (1 * 3 + z * 3) -24 + 16z = (3 + 3z) Solving -24 + 16z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -24 + 16z + -3z = 3 + 3z + -3z Combine like terms: 16z + -3z = 13z -24 + 13z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -24 + 13z = 3 + 0 -24 + 13z = 3 Add '24' to each side of the equation. -24 + 24 + 13z = 3 + 24 Combine like terms: -24 + 24 = 0 0 + 13z = 3 + 24 13z = 3 + 24 Combine like terms: 3 + 24 = 27 13z = 27 Divide each side by '13'. z = 2.076923077 Simplifying z = 2.076923077
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