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Simplifying 5(4z + -1) + -4(z + 8) = 12(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 8) = 12(z + 1) (-1 * 5 + 4z * 5) + -4(z + 8) = 12(z + 1) (-5 + 20z) + -4(z + 8) = 12(z + 1) Reorder the terms: -5 + 20z + -4(8 + z) = 12(z + 1) -5 + 20z + (8 * -4 + z * -4) = 12(z + 1) -5 + 20z + (-32 + -4z) = 12(z + 1) Reorder the terms: -5 + -32 + 20z + -4z = 12(z + 1) Combine like terms: -5 + -32 = -37 -37 + 20z + -4z = 12(z + 1) Combine like terms: 20z + -4z = 16z -37 + 16z = 12(z + 1) Reorder the terms: -37 + 16z = 12(1 + z) -37 + 16z = (1 * 12 + z * 12) -37 + 16z = (12 + 12z) Solving -37 + 16z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -37 + 16z + -12z = 12 + 12z + -12z Combine like terms: 16z + -12z = 4z -37 + 4z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -37 + 4z = 12 + 0 -37 + 4z = 12 Add '37' to each side of the equation. -37 + 37 + 4z = 12 + 37 Combine like terms: -37 + 37 = 0 0 + 4z = 12 + 37 4z = 12 + 37 Combine like terms: 12 + 37 = 49 4z = 49 Divide each side by '4'. z = 12.25 Simplifying z = 12.25
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