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Simplifying 6(3z + -1) + -2(z + 7) = 11(z + 1) Reorder the terms: 6(-1 + 3z) + -2(z + 7) = 11(z + 1) (-1 * 6 + 3z * 6) + -2(z + 7) = 11(z + 1) (-6 + 18z) + -2(z + 7) = 11(z + 1) Reorder the terms: -6 + 18z + -2(7 + z) = 11(z + 1) -6 + 18z + (7 * -2 + z * -2) = 11(z + 1) -6 + 18z + (-14 + -2z) = 11(z + 1) Reorder the terms: -6 + -14 + 18z + -2z = 11(z + 1) Combine like terms: -6 + -14 = -20 -20 + 18z + -2z = 11(z + 1) Combine like terms: 18z + -2z = 16z -20 + 16z = 11(z + 1) Reorder the terms: -20 + 16z = 11(1 + z) -20 + 16z = (1 * 11 + z * 11) -20 + 16z = (11 + 11z) Solving -20 + 16z = 11 + 11z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11z' to each side of the equation. -20 + 16z + -11z = 11 + 11z + -11z Combine like terms: 16z + -11z = 5z -20 + 5z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -20 + 5z = 11 + 0 -20 + 5z = 11 Add '20' to each side of the equation. -20 + 20 + 5z = 11 + 20 Combine like terms: -20 + 20 = 0 0 + 5z = 11 + 20 5z = 11 + 20 Combine like terms: 11 + 20 = 31 5z = 31 Divide each side by '5'. z = 6.2 Simplifying z = 6.2
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