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Simplifying 5(6z + -1) + -4(z + 6) = 8(z + 1) Reorder the terms: 5(-1 + 6z) + -4(z + 6) = 8(z + 1) (-1 * 5 + 6z * 5) + -4(z + 6) = 8(z + 1) (-5 + 30z) + -4(z + 6) = 8(z + 1) Reorder the terms: -5 + 30z + -4(6 + z) = 8(z + 1) -5 + 30z + (6 * -4 + z * -4) = 8(z + 1) -5 + 30z + (-24 + -4z) = 8(z + 1) Reorder the terms: -5 + -24 + 30z + -4z = 8(z + 1) Combine like terms: -5 + -24 = -29 -29 + 30z + -4z = 8(z + 1) Combine like terms: 30z + -4z = 26z -29 + 26z = 8(z + 1) Reorder the terms: -29 + 26z = 8(1 + z) -29 + 26z = (1 * 8 + z * 8) -29 + 26z = (8 + 8z) Solving -29 + 26z = 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. -29 + 26z + -8z = 8 + 8z + -8z Combine like terms: 26z + -8z = 18z -29 + 18z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -29 + 18z = 8 + 0 -29 + 18z = 8 Add '29' to each side of the equation. -29 + 29 + 18z = 8 + 29 Combine like terms: -29 + 29 = 0 0 + 18z = 8 + 29 18z = 8 + 29 Combine like terms: 8 + 29 = 37 18z = 37 Divide each side by '18'. z = 2.055555556 Simplifying z = 2.055555556
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