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Simplifying 3(6z + -1) + -5(z + 7) = 8(z + 1) Reorder the terms: 3(-1 + 6z) + -5(z + 7) = 8(z + 1) (-1 * 3 + 6z * 3) + -5(z + 7) = 8(z + 1) (-3 + 18z) + -5(z + 7) = 8(z + 1) Reorder the terms: -3 + 18z + -5(7 + z) = 8(z + 1) -3 + 18z + (7 * -5 + z * -5) = 8(z + 1) -3 + 18z + (-35 + -5z) = 8(z + 1) Reorder the terms: -3 + -35 + 18z + -5z = 8(z + 1) Combine like terms: -3 + -35 = -38 -38 + 18z + -5z = 8(z + 1) Combine like terms: 18z + -5z = 13z -38 + 13z = 8(z + 1) Reorder the terms: -38 + 13z = 8(1 + z) -38 + 13z = (1 * 8 + z * 8) -38 + 13z = (8 + 8z) Solving -38 + 13z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -38 + 13z + -8z = 8 + 8z + -8z Combine like terms: 13z + -8z = 5z -38 + 5z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -38 + 5z = 8 + 0 -38 + 5z = 8 Add '38' to each side of the equation. -38 + 38 + 5z = 8 + 38 Combine like terms: -38 + 38 = 0 0 + 5z = 8 + 38 5z = 8 + 38 Combine like terms: 8 + 38 = 46 5z = 46 Divide each side by '5'. z = 9.2 Simplifying z = 9.2
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