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Simplifying 5(4z + -1) + -4(z + 8) = 5(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 8) = 5(z + 1) (-1 * 5 + 4z * 5) + -4(z + 8) = 5(z + 1) (-5 + 20z) + -4(z + 8) = 5(z + 1) Reorder the terms: -5 + 20z + -4(8 + z) = 5(z + 1) -5 + 20z + (8 * -4 + z * -4) = 5(z + 1) -5 + 20z + (-32 + -4z) = 5(z + 1) Reorder the terms: -5 + -32 + 20z + -4z = 5(z + 1) Combine like terms: -5 + -32 = -37 -37 + 20z + -4z = 5(z + 1) Combine like terms: 20z + -4z = 16z -37 + 16z = 5(z + 1) Reorder the terms: -37 + 16z = 5(1 + z) -37 + 16z = (1 * 5 + z * 5) -37 + 16z = (5 + 5z) Solving -37 + 16z = 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. -37 + 16z + -5z = 5 + 5z + -5z Combine like terms: 16z + -5z = 11z -37 + 11z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -37 + 11z = 5 + 0 -37 + 11z = 5 Add '37' to each side of the equation. -37 + 37 + 11z = 5 + 37 Combine like terms: -37 + 37 = 0 0 + 11z = 5 + 37 11z = 5 + 37 Combine like terms: 5 + 37 = 42 11z = 42 Divide each side by '11'. z = 3.818181818 Simplifying z = 3.818181818
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