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Simplifying 5(6z + -1) + -5(z + 1) = 14(z + 1) Reorder the terms: 5(-1 + 6z) + -5(z + 1) = 14(z + 1) (-1 * 5 + 6z * 5) + -5(z + 1) = 14(z + 1) (-5 + 30z) + -5(z + 1) = 14(z + 1) Reorder the terms: -5 + 30z + -5(1 + z) = 14(z + 1) -5 + 30z + (1 * -5 + z * -5) = 14(z + 1) -5 + 30z + (-5 + -5z) = 14(z + 1) Reorder the terms: -5 + -5 + 30z + -5z = 14(z + 1) Combine like terms: -5 + -5 = -10 -10 + 30z + -5z = 14(z + 1) Combine like terms: 30z + -5z = 25z -10 + 25z = 14(z + 1) Reorder the terms: -10 + 25z = 14(1 + z) -10 + 25z = (1 * 14 + z * 14) -10 + 25z = (14 + 14z) Solving -10 + 25z = 14 + 14z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14z' to each side of the equation. -10 + 25z + -14z = 14 + 14z + -14z Combine like terms: 25z + -14z = 11z -10 + 11z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -10 + 11z = 14 + 0 -10 + 11z = 14 Add '10' to each side of the equation. -10 + 10 + 11z = 14 + 10 Combine like terms: -10 + 10 = 0 0 + 11z = 14 + 10 11z = 14 + 10 Combine like terms: 14 + 10 = 24 11z = 24 Divide each side by '11'. z = 2.181818182 Simplifying z = 2.181818182
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