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Simplifying 3(z + -1(4z + 9) + 6) = 4(z + 1) Reorder the terms: 3(z + -1(9 + 4z) + 6) = 4(z + 1) 3(z + (9 * -1 + 4z * -1) + 6) = 4(z + 1) 3(z + (-9 + -4z) + 6) = 4(z + 1) Reorder the terms: 3(-9 + 6 + z + -4z) = 4(z + 1) Combine like terms: -9 + 6 = -3 3(-3 + z + -4z) = 4(z + 1) Combine like terms: z + -4z = -3z 3(-3 + -3z) = 4(z + 1) (-3 * 3 + -3z * 3) = 4(z + 1) (-9 + -9z) = 4(z + 1) Reorder the terms: -9 + -9z = 4(1 + z) -9 + -9z = (1 * 4 + z * 4) -9 + -9z = (4 + 4z) Solving -9 + -9z = 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. -9 + -9z + -4z = 4 + 4z + -4z Combine like terms: -9z + -4z = -13z -9 + -13z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -9 + -13z = 4 + 0 -9 + -13z = 4 Add '9' to each side of the equation. -9 + 9 + -13z = 4 + 9 Combine like terms: -9 + 9 = 0 0 + -13z = 4 + 9 -13z = 4 + 9 Combine like terms: 4 + 9 = 13 -13z = 13 Divide each side by '-13'. z = -1 Simplifying z = -1
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