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Simplifying -1(z + 8) + (5z + 1) = -4(z + 1) Reorder the terms: -1(8 + z) + (5z + 1) = -4(z + 1) (8 * -1 + z * -1) + (5z + 1) = -4(z + 1) (-8 + -1z) + (5z + 1) = -4(z + 1) Reorder the terms: -8 + -1z + (1 + 5z) = -4(z + 1) Remove parenthesis around (1 + 5z) -8 + -1z + 1 + 5z = -4(z + 1) Reorder the terms: -8 + 1 + -1z + 5z = -4(z + 1) Combine like terms: -8 + 1 = -7 -7 + -1z + 5z = -4(z + 1) Combine like terms: -1z + 5z = 4z -7 + 4z = -4(z + 1) Reorder the terms: -7 + 4z = -4(1 + z) -7 + 4z = (1 * -4 + z * -4) -7 + 4z = (-4 + -4z) Solving -7 + 4z = -4 + -4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4z' to each side of the equation. -7 + 4z + 4z = -4 + -4z + 4z Combine like terms: 4z + 4z = 8z -7 + 8z = -4 + -4z + 4z Combine like terms: -4z + 4z = 0 -7 + 8z = -4 + 0 -7 + 8z = -4 Add '7' to each side of the equation. -7 + 7 + 8z = -4 + 7 Combine like terms: -7 + 7 = 0 0 + 8z = -4 + 7 8z = -4 + 7 Combine like terms: -4 + 7 = 3 8z = 3 Divide each side by '8'. z = 0.375 Simplifying z = 0.375
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