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Simplifying 6(3z + -1) + -5(z + 9) = 4(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 9) = 4(z + 1) (-1 * 6 + 3z * 6) + -5(z + 9) = 4(z + 1) (-6 + 18z) + -5(z + 9) = 4(z + 1) Reorder the terms: -6 + 18z + -5(9 + z) = 4(z + 1) -6 + 18z + (9 * -5 + z * -5) = 4(z + 1) -6 + 18z + (-45 + -5z) = 4(z + 1) Reorder the terms: -6 + -45 + 18z + -5z = 4(z + 1) Combine like terms: -6 + -45 = -51 -51 + 18z + -5z = 4(z + 1) Combine like terms: 18z + -5z = 13z -51 + 13z = 4(z + 1) Reorder the terms: -51 + 13z = 4(1 + z) -51 + 13z = (1 * 4 + z * 4) -51 + 13z = (4 + 4z) Solving -51 + 13z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -51 + 13z + -4z = 4 + 4z + -4z Combine like terms: 13z + -4z = 9z -51 + 9z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -51 + 9z = 4 + 0 -51 + 9z = 4 Add '51' to each side of the equation. -51 + 51 + 9z = 4 + 51 Combine like terms: -51 + 51 = 0 0 + 9z = 4 + 51 9z = 4 + 51 Combine like terms: 4 + 51 = 55 9z = 55 Divide each side by '9'. z = 6.111111111 Simplifying z = 6.111111111
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