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Simplifying 6(3z + -1) + -5(z + 3) = 8(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 3) = 8(z + 1) (-1 * 6 + 3z * 6) + -5(z + 3) = 8(z + 1) (-6 + 18z) + -5(z + 3) = 8(z + 1) Reorder the terms: -6 + 18z + -5(3 + z) = 8(z + 1) -6 + 18z + (3 * -5 + z * -5) = 8(z + 1) -6 + 18z + (-15 + -5z) = 8(z + 1) Reorder the terms: -6 + -15 + 18z + -5z = 8(z + 1) Combine like terms: -6 + -15 = -21 -21 + 18z + -5z = 8(z + 1) Combine like terms: 18z + -5z = 13z -21 + 13z = 8(z + 1) Reorder the terms: -21 + 13z = 8(1 + z) -21 + 13z = (1 * 8 + z * 8) -21 + 13z = (8 + 8z) Solving -21 + 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. -21 + 13z + -8z = 8 + 8z + -8z Combine like terms: 13z + -8z = 5z -21 + 5z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -21 + 5z = 8 + 0 -21 + 5z = 8 Add '21' to each side of the equation. -21 + 21 + 5z = 8 + 21 Combine like terms: -21 + 21 = 0 0 + 5z = 8 + 21 5z = 8 + 21 Combine like terms: 8 + 21 = 29 5z = 29 Divide each side by '5'. z = 5.8 Simplifying z = 5.8
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