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Simplifying -1(z + 5) + (6z + 1) = 3(z + 1) Reorder the terms: -1(5 + z) + (6z + 1) = 3(z + 1) (5 * -1 + z * -1) + (6z + 1) = 3(z + 1) (-5 + -1z) + (6z + 1) = 3(z + 1) Reorder the terms: -5 + -1z + (1 + 6z) = 3(z + 1) Remove parenthesis around (1 + 6z) -5 + -1z + 1 + 6z = 3(z + 1) Reorder the terms: -5 + 1 + -1z + 6z = 3(z + 1) Combine like terms: -5 + 1 = -4 -4 + -1z + 6z = 3(z + 1) Combine like terms: -1z + 6z = 5z -4 + 5z = 3(z + 1) Reorder the terms: -4 + 5z = 3(1 + z) -4 + 5z = (1 * 3 + z * 3) -4 + 5z = (3 + 3z) Solving -4 + 5z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -4 + 5z + -3z = 3 + 3z + -3z Combine like terms: 5z + -3z = 2z -4 + 2z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -4 + 2z = 3 + 0 -4 + 2z = 3 Add '4' to each side of the equation. -4 + 4 + 2z = 3 + 4 Combine like terms: -4 + 4 = 0 0 + 2z = 3 + 4 2z = 3 + 4 Combine like terms: 3 + 4 = 7 2z = 7 Divide each side by '2'. z = 3.5 Simplifying z = 3.5
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