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Simplifying 6(3z + -1) + -4(z + 3) = 5(z + 1) Reorder the terms: 6(-1 + 3z) + -4(z + 3) = 5(z + 1) (-1 * 6 + 3z * 6) + -4(z + 3) = 5(z + 1) (-6 + 18z) + -4(z + 3) = 5(z + 1) Reorder the terms: -6 + 18z + -4(3 + z) = 5(z + 1) -6 + 18z + (3 * -4 + z * -4) = 5(z + 1) -6 + 18z + (-12 + -4z) = 5(z + 1) Reorder the terms: -6 + -12 + 18z + -4z = 5(z + 1) Combine like terms: -6 + -12 = -18 -18 + 18z + -4z = 5(z + 1) Combine like terms: 18z + -4z = 14z -18 + 14z = 5(z + 1) Reorder the terms: -18 + 14z = 5(1 + z) -18 + 14z = (1 * 5 + z * 5) -18 + 14z = (5 + 5z) Solving -18 + 14z = 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. -18 + 14z + -5z = 5 + 5z + -5z Combine like terms: 14z + -5z = 9z -18 + 9z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -18 + 9z = 5 + 0 -18 + 9z = 5 Add '18' to each side of the equation. -18 + 18 + 9z = 5 + 18 Combine like terms: -18 + 18 = 0 0 + 9z = 5 + 18 9z = 5 + 18 Combine like terms: 5 + 18 = 23 9z = 23 Divide each side by '9'. z = 2.555555556 Simplifying z = 2.555555556
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