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Simplifying -1(z + 5) + (4z + 1) = 2(z + 1) Reorder the terms: -1(5 + z) + (4z + 1) = 2(z + 1) (5 * -1 + z * -1) + (4z + 1) = 2(z + 1) (-5 + -1z) + (4z + 1) = 2(z + 1) Reorder the terms: -5 + -1z + (1 + 4z) = 2(z + 1) Remove parenthesis around (1 + 4z) -5 + -1z + 1 + 4z = 2(z + 1) Reorder the terms: -5 + 1 + -1z + 4z = 2(z + 1) Combine like terms: -5 + 1 = -4 -4 + -1z + 4z = 2(z + 1) Combine like terms: -1z + 4z = 3z -4 + 3z = 2(z + 1) Reorder the terms: -4 + 3z = 2(1 + z) -4 + 3z = (1 * 2 + z * 2) -4 + 3z = (2 + 2z) Solving -4 + 3z = 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. -4 + 3z + -2z = 2 + 2z + -2z Combine like terms: 3z + -2z = 1z -4 + 1z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -4 + 1z = 2 + 0 -4 + 1z = 2 Add '4' to each side of the equation. -4 + 4 + 1z = 2 + 4 Combine like terms: -4 + 4 = 0 0 + 1z = 2 + 4 1z = 2 + 4 Combine like terms: 2 + 4 = 6 1z = 6 Divide each side by '1'. z = 6 Simplifying z = 6
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