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Simplifying -1(z + 8) + (2z + 1) = -2(z + 1) Reorder the terms: -1(8 + z) + (2z + 1) = -2(z + 1) (8 * -1 + z * -1) + (2z + 1) = -2(z + 1) (-8 + -1z) + (2z + 1) = -2(z + 1) Reorder the terms: -8 + -1z + (1 + 2z) = -2(z + 1) Remove parenthesis around (1 + 2z) -8 + -1z + 1 + 2z = -2(z + 1) Reorder the terms: -8 + 1 + -1z + 2z = -2(z + 1) Combine like terms: -8 + 1 = -7 -7 + -1z + 2z = -2(z + 1) Combine like terms: -1z + 2z = 1z -7 + 1z = -2(z + 1) Reorder the terms: -7 + 1z = -2(1 + z) -7 + 1z = (1 * -2 + z * -2) -7 + 1z = (-2 + -2z) Solving -7 + 1z = -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. -7 + 1z + 2z = -2 + -2z + 2z Combine like terms: 1z + 2z = 3z -7 + 3z = -2 + -2z + 2z Combine like terms: -2z + 2z = 0 -7 + 3z = -2 + 0 -7 + 3z = -2 Add '7' to each side of the equation. -7 + 7 + 3z = -2 + 7 Combine like terms: -7 + 7 = 0 0 + 3z = -2 + 7 3z = -2 + 7 Combine like terms: -2 + 7 = 5 3z = 5 Divide each side by '3'. z = 1.666666667 Simplifying z = 1.666666667
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