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Simplifying 6(3z + -1) + -4(z + 9) = 11(z + 1) Reorder the terms: 6(-1 + 3z) + -4(z + 9) = 11(z + 1) (-1 * 6 + 3z * 6) + -4(z + 9) = 11(z + 1) (-6 + 18z) + -4(z + 9) = 11(z + 1) Reorder the terms: -6 + 18z + -4(9 + z) = 11(z + 1) -6 + 18z + (9 * -4 + z * -4) = 11(z + 1) -6 + 18z + (-36 + -4z) = 11(z + 1) Reorder the terms: -6 + -36 + 18z + -4z = 11(z + 1) Combine like terms: -6 + -36 = -42 -42 + 18z + -4z = 11(z + 1) Combine like terms: 18z + -4z = 14z -42 + 14z = 11(z + 1) Reorder the terms: -42 + 14z = 11(1 + z) -42 + 14z = (1 * 11 + z * 11) -42 + 14z = (11 + 11z) Solving -42 + 14z = 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. -42 + 14z + -11z = 11 + 11z + -11z Combine like terms: 14z + -11z = 3z -42 + 3z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -42 + 3z = 11 + 0 -42 + 3z = 11 Add '42' to each side of the equation. -42 + 42 + 3z = 11 + 42 Combine like terms: -42 + 42 = 0 0 + 3z = 11 + 42 3z = 11 + 42 Combine like terms: 11 + 42 = 53 3z = 53 Divide each side by '3'. z = 17.66666667 Simplifying z = 17.66666667
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