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Simplifying 3(6z + -1) + -4(z + 5) = 6(z + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 5) = 6(z + 1) (-1 * 3 + 6z * 3) + -4(z + 5) = 6(z + 1) (-3 + 18z) + -4(z + 5) = 6(z + 1) Reorder the terms: -3 + 18z + -4(5 + z) = 6(z + 1) -3 + 18z + (5 * -4 + z * -4) = 6(z + 1) -3 + 18z + (-20 + -4z) = 6(z + 1) Reorder the terms: -3 + -20 + 18z + -4z = 6(z + 1) Combine like terms: -3 + -20 = -23 -23 + 18z + -4z = 6(z + 1) Combine like terms: 18z + -4z = 14z -23 + 14z = 6(z + 1) Reorder the terms: -23 + 14z = 6(1 + z) -23 + 14z = (1 * 6 + z * 6) -23 + 14z = (6 + 6z) Solving -23 + 14z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -23 + 14z + -6z = 6 + 6z + -6z Combine like terms: 14z + -6z = 8z -23 + 8z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -23 + 8z = 6 + 0 -23 + 8z = 6 Add '23' to each side of the equation. -23 + 23 + 8z = 6 + 23 Combine like terms: -23 + 23 = 0 0 + 8z = 6 + 23 8z = 6 + 23 Combine like terms: 6 + 23 = 29 8z = 29 Divide each side by '8'. z = 3.625 Simplifying z = 3.625
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