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Simplifying -1(z + 7) + (4z + 1) = -5(z + 1) Reorder the terms: -1(7 + z) + (4z + 1) = -5(z + 1) (7 * -1 + z * -1) + (4z + 1) = -5(z + 1) (-7 + -1z) + (4z + 1) = -5(z + 1) Reorder the terms: -7 + -1z + (1 + 4z) = -5(z + 1) Remove parenthesis around (1 + 4z) -7 + -1z + 1 + 4z = -5(z + 1) Reorder the terms: -7 + 1 + -1z + 4z = -5(z + 1) Combine like terms: -7 + 1 = -6 -6 + -1z + 4z = -5(z + 1) Combine like terms: -1z + 4z = 3z -6 + 3z = -5(z + 1) Reorder the terms: -6 + 3z = -5(1 + z) -6 + 3z = (1 * -5 + z * -5) -6 + 3z = (-5 + -5z) Solving -6 + 3z = -5 + -5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5z' to each side of the equation. -6 + 3z + 5z = -5 + -5z + 5z Combine like terms: 3z + 5z = 8z -6 + 8z = -5 + -5z + 5z Combine like terms: -5z + 5z = 0 -6 + 8z = -5 + 0 -6 + 8z = -5 Add '6' to each side of the equation. -6 + 6 + 8z = -5 + 6 Combine like terms: -6 + 6 = 0 0 + 8z = -5 + 6 8z = -5 + 6 Combine like terms: -5 + 6 = 1 8z = 1 Divide each side by '8'. z = 0.125 Simplifying z = 0.125
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