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Simplifying 3(6z + -1) + -3(z + 5) = 11(z + 1) Reorder the terms: 3(-1 + 6z) + -3(z + 5) = 11(z + 1) (-1 * 3 + 6z * 3) + -3(z + 5) = 11(z + 1) (-3 + 18z) + -3(z + 5) = 11(z + 1) Reorder the terms: -3 + 18z + -3(5 + z) = 11(z + 1) -3 + 18z + (5 * -3 + z * -3) = 11(z + 1) -3 + 18z + (-15 + -3z) = 11(z + 1) Reorder the terms: -3 + -15 + 18z + -3z = 11(z + 1) Combine like terms: -3 + -15 = -18 -18 + 18z + -3z = 11(z + 1) Combine like terms: 18z + -3z = 15z -18 + 15z = 11(z + 1) Reorder the terms: -18 + 15z = 11(1 + z) -18 + 15z = (1 * 11 + z * 11) -18 + 15z = (11 + 11z) Solving -18 + 15z = 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. -18 + 15z + -11z = 11 + 11z + -11z Combine like terms: 15z + -11z = 4z -18 + 4z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -18 + 4z = 11 + 0 -18 + 4z = 11 Add '18' to each side of the equation. -18 + 18 + 4z = 11 + 18 Combine like terms: -18 + 18 = 0 0 + 4z = 11 + 18 4z = 11 + 18 Combine like terms: 11 + 18 = 29 4z = 29 Divide each side by '4'. z = 7.25 Simplifying z = 7.25
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