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Simplifying 3(6z + -1) + -5(z + 7) = 9(z + 1) Reorder the terms: 3(-1 + 6z) + -5(z + 7) = 9(z + 1) (-1 * 3 + 6z * 3) + -5(z + 7) = 9(z + 1) (-3 + 18z) + -5(z + 7) = 9(z + 1) Reorder the terms: -3 + 18z + -5(7 + z) = 9(z + 1) -3 + 18z + (7 * -5 + z * -5) = 9(z + 1) -3 + 18z + (-35 + -5z) = 9(z + 1) Reorder the terms: -3 + -35 + 18z + -5z = 9(z + 1) Combine like terms: -3 + -35 = -38 -38 + 18z + -5z = 9(z + 1) Combine like terms: 18z + -5z = 13z -38 + 13z = 9(z + 1) Reorder the terms: -38 + 13z = 9(1 + z) -38 + 13z = (1 * 9 + z * 9) -38 + 13z = (9 + 9z) Solving -38 + 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. -38 + 13z + -9z = 9 + 9z + -9z Combine like terms: 13z + -9z = 4z -38 + 4z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -38 + 4z = 9 + 0 -38 + 4z = 9 Add '38' to each side of the equation. -38 + 38 + 4z = 9 + 38 Combine like terms: -38 + 38 = 0 0 + 4z = 9 + 38 4z = 9 + 38 Combine like terms: 9 + 38 = 47 4z = 47 Divide each side by '4'. z = 11.75 Simplifying z = 11.75
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