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Simplifying 6(3z + -1) + -2(z + 4) = 5(z + 1) Reorder the terms: 6(-1 + 3z) + -2(z + 4) = 5(z + 1) (-1 * 6 + 3z * 6) + -2(z + 4) = 5(z + 1) (-6 + 18z) + -2(z + 4) = 5(z + 1) Reorder the terms: -6 + 18z + -2(4 + z) = 5(z + 1) -6 + 18z + (4 * -2 + z * -2) = 5(z + 1) -6 + 18z + (-8 + -2z) = 5(z + 1) Reorder the terms: -6 + -8 + 18z + -2z = 5(z + 1) Combine like terms: -6 + -8 = -14 -14 + 18z + -2z = 5(z + 1) Combine like terms: 18z + -2z = 16z -14 + 16z = 5(z + 1) Reorder the terms: -14 + 16z = 5(1 + z) -14 + 16z = (1 * 5 + z * 5) -14 + 16z = (5 + 5z) Solving -14 + 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. -14 + 16z + -5z = 5 + 5z + -5z Combine like terms: 16z + -5z = 11z -14 + 11z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -14 + 11z = 5 + 0 -14 + 11z = 5 Add '14' to each side of the equation. -14 + 14 + 11z = 5 + 14 Combine like terms: -14 + 14 = 0 0 + 11z = 5 + 14 11z = 5 + 14 Combine like terms: 5 + 14 = 19 11z = 19 Divide each side by '11'. z = 1.727272727 Simplifying z = 1.727272727
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