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Simplifying 5(6z + -1) + -2(z + 5) = 23(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 5) = 23(z + 1) (-1 * 5 + 6z * 5) + -2(z + 5) = 23(z + 1) (-5 + 30z) + -2(z + 5) = 23(z + 1) Reorder the terms: -5 + 30z + -2(5 + z) = 23(z + 1) -5 + 30z + (5 * -2 + z * -2) = 23(z + 1) -5 + 30z + (-10 + -2z) = 23(z + 1) Reorder the terms: -5 + -10 + 30z + -2z = 23(z + 1) Combine like terms: -5 + -10 = -15 -15 + 30z + -2z = 23(z + 1) Combine like terms: 30z + -2z = 28z -15 + 28z = 23(z + 1) Reorder the terms: -15 + 28z = 23(1 + z) -15 + 28z = (1 * 23 + z * 23) -15 + 28z = (23 + 23z) Solving -15 + 28z = 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. -15 + 28z + -23z = 23 + 23z + -23z Combine like terms: 28z + -23z = 5z -15 + 5z = 23 + 23z + -23z Combine like terms: 23z + -23z = 0 -15 + 5z = 23 + 0 -15 + 5z = 23 Add '15' to each side of the equation. -15 + 15 + 5z = 23 + 15 Combine like terms: -15 + 15 = 0 0 + 5z = 23 + 15 5z = 23 + 15 Combine like terms: 23 + 15 = 38 5z = 38 Divide each side by '5'. z = 7.6 Simplifying z = 7.6
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