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Simplifying 5(6z + -1) + -5(z + 1) = 23(z + 1) Reorder the terms: 5(-1 + 6z) + -5(z + 1) = 23(z + 1) (-1 * 5 + 6z * 5) + -5(z + 1) = 23(z + 1) (-5 + 30z) + -5(z + 1) = 23(z + 1) Reorder the terms: -5 + 30z + -5(1 + z) = 23(z + 1) -5 + 30z + (1 * -5 + z * -5) = 23(z + 1) -5 + 30z + (-5 + -5z) = 23(z + 1) Reorder the terms: -5 + -5 + 30z + -5z = 23(z + 1) Combine like terms: -5 + -5 = -10 -10 + 30z + -5z = 23(z + 1) Combine like terms: 30z + -5z = 25z -10 + 25z = 23(z + 1) Reorder the terms: -10 + 25z = 23(1 + z) -10 + 25z = (1 * 23 + z * 23) -10 + 25z = (23 + 23z) Solving -10 + 25z = 23 + 23z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-23z' to each side of the equation. -10 + 25z + -23z = 23 + 23z + -23z Combine like terms: 25z + -23z = 2z -10 + 2z = 23 + 23z + -23z Combine like terms: 23z + -23z = 0 -10 + 2z = 23 + 0 -10 + 2z = 23 Add '10' to each side of the equation. -10 + 10 + 2z = 23 + 10 Combine like terms: -10 + 10 = 0 0 + 2z = 23 + 10 2z = 23 + 10 Combine like terms: 23 + 10 = 33 2z = 33 Divide each side by '2'. z = 16.5 Simplifying z = 16.5
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