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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 = 8z -4 + 8z = -3 + -3z + 3z Combine like terms: -3z + 3z = 0 -4 + 8z = -3 + 0 -4 + 8z = -3 Add '4' to each side of the equation. -4 + 4 + 8z = -3 + 4 Combine like terms: -4 + 4 = 0 0 + 8z = -3 + 4 8z = -3 + 4 Combine like terms: -3 + 4 = 1 8z = 1 Divide each side by '8'. z = 0.125 Simplifying z = 0.125
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