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Simplifying -1(z + 8) + (3z + 1) = 6(z + 1) Reorder the terms: -1(8 + z) + (3z + 1) = 6(z + 1) (8 * -1 + z * -1) + (3z + 1) = 6(z + 1) (-8 + -1z) + (3z + 1) = 6(z + 1) Reorder the terms: -8 + -1z + (1 + 3z) = 6(z + 1) Remove parenthesis around (1 + 3z) -8 + -1z + 1 + 3z = 6(z + 1) Reorder the terms: -8 + 1 + -1z + 3z = 6(z + 1) Combine like terms: -8 + 1 = -7 -7 + -1z + 3z = 6(z + 1) Combine like terms: -1z + 3z = 2z -7 + 2z = 6(z + 1) Reorder the terms: -7 + 2z = 6(1 + z) -7 + 2z = (1 * 6 + z * 6) -7 + 2z = (6 + 6z) Solving -7 + 2z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -7 + 2z + -6z = 6 + 6z + -6z Combine like terms: 2z + -6z = -4z -7 + -4z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -7 + -4z = 6 + 0 -7 + -4z = 6 Add '7' to each side of the equation. -7 + 7 + -4z = 6 + 7 Combine like terms: -7 + 7 = 0 0 + -4z = 6 + 7 -4z = 6 + 7 Combine like terms: 6 + 7 = 13 -4z = 13 Divide each side by '-4'. z = -3.25 Simplifying z = -3.25
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