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Simplifying 5(6z + -1) + -2(z + 9) = 8(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 9) = 8(z + 1) (-1 * 5 + 6z * 5) + -2(z + 9) = 8(z + 1) (-5 + 30z) + -2(z + 9) = 8(z + 1) Reorder the terms: -5 + 30z + -2(9 + z) = 8(z + 1) -5 + 30z + (9 * -2 + z * -2) = 8(z + 1) -5 + 30z + (-18 + -2z) = 8(z + 1) Reorder the terms: -5 + -18 + 30z + -2z = 8(z + 1) Combine like terms: -5 + -18 = -23 -23 + 30z + -2z = 8(z + 1) Combine like terms: 30z + -2z = 28z -23 + 28z = 8(z + 1) Reorder the terms: -23 + 28z = 8(1 + z) -23 + 28z = (1 * 8 + z * 8) -23 + 28z = (8 + 8z) Solving -23 + 28z = 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. -23 + 28z + -8z = 8 + 8z + -8z Combine like terms: 28z + -8z = 20z -23 + 20z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -23 + 20z = 8 + 0 -23 + 20z = 8 Add '23' to each side of the equation. -23 + 23 + 20z = 8 + 23 Combine like terms: -23 + 23 = 0 0 + 20z = 8 + 23 20z = 8 + 23 Combine like terms: 8 + 23 = 31 20z = 31 Divide each side by '20'. z = 1.55 Simplifying z = 1.55
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