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Simplifying 5(3z + -1) + -5(z + 6) = 2(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 6) = 2(z + 1) (-1 * 5 + 3z * 5) + -5(z + 6) = 2(z + 1) (-5 + 15z) + -5(z + 6) = 2(z + 1) Reorder the terms: -5 + 15z + -5(6 + z) = 2(z + 1) -5 + 15z + (6 * -5 + z * -5) = 2(z + 1) -5 + 15z + (-30 + -5z) = 2(z + 1) Reorder the terms: -5 + -30 + 15z + -5z = 2(z + 1) Combine like terms: -5 + -30 = -35 -35 + 15z + -5z = 2(z + 1) Combine like terms: 15z + -5z = 10z -35 + 10z = 2(z + 1) Reorder the terms: -35 + 10z = 2(1 + z) -35 + 10z = (1 * 2 + z * 2) -35 + 10z = (2 + 2z) Solving -35 + 10z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -35 + 10z + -2z = 2 + 2z + -2z Combine like terms: 10z + -2z = 8z -35 + 8z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -35 + 8z = 2 + 0 -35 + 8z = 2 Add '35' to each side of the equation. -35 + 35 + 8z = 2 + 35 Combine like terms: -35 + 35 = 0 0 + 8z = 2 + 35 8z = 2 + 35 Combine like terms: 2 + 35 = 37 8z = 37 Divide each side by '8'. z = 4.625 Simplifying z = 4.625
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