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Simplifying 5(2z + 1) + -2(z + 5) = 6(z + 1) Reorder the terms: 5(1 + 2z) + -2(z + 5) = 6(z + 1) (1 * 5 + 2z * 5) + -2(z + 5) = 6(z + 1) (5 + 10z) + -2(z + 5) = 6(z + 1) Reorder the terms: 5 + 10z + -2(5 + z) = 6(z + 1) 5 + 10z + (5 * -2 + z * -2) = 6(z + 1) 5 + 10z + (-10 + -2z) = 6(z + 1) Reorder the terms: 5 + -10 + 10z + -2z = 6(z + 1) Combine like terms: 5 + -10 = -5 -5 + 10z + -2z = 6(z + 1) Combine like terms: 10z + -2z = 8z -5 + 8z = 6(z + 1) Reorder the terms: -5 + 8z = 6(1 + z) -5 + 8z = (1 * 6 + z * 6) -5 + 8z = (6 + 6z) Solving -5 + 8z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -5 + 8z + -6z = 6 + 6z + -6z Combine like terms: 8z + -6z = 2z -5 + 2z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -5 + 2z = 6 + 0 -5 + 2z = 6 Add '5' to each side of the equation. -5 + 5 + 2z = 6 + 5 Combine like terms: -5 + 5 = 0 0 + 2z = 6 + 5 2z = 6 + 5 Combine like terms: 6 + 5 = 11 2z = 11 Divide each side by '2'. z = 5.5 Simplifying z = 5.5
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