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Simplifying 5(6z + -1) + -4(z + 4) = 12(z + 1) Reorder the terms: 5(-1 + 6z) + -4(z + 4) = 12(z + 1) (-1 * 5 + 6z * 5) + -4(z + 4) = 12(z + 1) (-5 + 30z) + -4(z + 4) = 12(z + 1) Reorder the terms: -5 + 30z + -4(4 + z) = 12(z + 1) -5 + 30z + (4 * -4 + z * -4) = 12(z + 1) -5 + 30z + (-16 + -4z) = 12(z + 1) Reorder the terms: -5 + -16 + 30z + -4z = 12(z + 1) Combine like terms: -5 + -16 = -21 -21 + 30z + -4z = 12(z + 1) Combine like terms: 30z + -4z = 26z -21 + 26z = 12(z + 1) Reorder the terms: -21 + 26z = 12(1 + z) -21 + 26z = (1 * 12 + z * 12) -21 + 26z = (12 + 12z) Solving -21 + 26z = 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. -21 + 26z + -12z = 12 + 12z + -12z Combine like terms: 26z + -12z = 14z -21 + 14z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -21 + 14z = 12 + 0 -21 + 14z = 12 Add '21' to each side of the equation. -21 + 21 + 14z = 12 + 21 Combine like terms: -21 + 21 = 0 0 + 14z = 12 + 21 14z = 12 + 21 Combine like terms: 12 + 21 = 33 14z = 33 Divide each side by '14'. z = 2.357142857 Simplifying z = 2.357142857
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