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Simplifying 6(3z + -1) + -5(z + 2) = 9(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 2) = 9(z + 1) (-1 * 6 + 3z * 6) + -5(z + 2) = 9(z + 1) (-6 + 18z) + -5(z + 2) = 9(z + 1) Reorder the terms: -6 + 18z + -5(2 + z) = 9(z + 1) -6 + 18z + (2 * -5 + z * -5) = 9(z + 1) -6 + 18z + (-10 + -5z) = 9(z + 1) Reorder the terms: -6 + -10 + 18z + -5z = 9(z + 1) Combine like terms: -6 + -10 = -16 -16 + 18z + -5z = 9(z + 1) Combine like terms: 18z + -5z = 13z -16 + 13z = 9(z + 1) Reorder the terms: -16 + 13z = 9(1 + z) -16 + 13z = (1 * 9 + z * 9) -16 + 13z = (9 + 9z) Solving -16 + 13z = 9 + 9z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9z' to each side of the equation. -16 + 13z + -9z = 9 + 9z + -9z Combine like terms: 13z + -9z = 4z -16 + 4z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -16 + 4z = 9 + 0 -16 + 4z = 9 Add '16' to each side of the equation. -16 + 16 + 4z = 9 + 16 Combine like terms: -16 + 16 = 0 0 + 4z = 9 + 16 4z = 9 + 16 Combine like terms: 9 + 16 = 25 4z = 25 Divide each side by '4'. z = 6.25 Simplifying z = 6.25
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