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Simplifying (5 + -3z) + -1(-4z + 6) = (8z + 11) + -1(3z + -6) Remove parenthesis around (5 + -3z) 5 + -3z + -1(-4z + 6) = (8z + 11) + -1(3z + -6) Reorder the terms: 5 + -3z + -1(6 + -4z) = (8z + 11) + -1(3z + -6) 5 + -3z + (6 * -1 + -4z * -1) = (8z + 11) + -1(3z + -6) 5 + -3z + (-6 + 4z) = (8z + 11) + -1(3z + -6) Reorder the terms: 5 + -6 + -3z + 4z = (8z + 11) + -1(3z + -6) Combine like terms: 5 + -6 = -1 -1 + -3z + 4z = (8z + 11) + -1(3z + -6) Combine like terms: -3z + 4z = 1z -1 + 1z = (8z + 11) + -1(3z + -6) Reorder the terms: -1 + 1z = (11 + 8z) + -1(3z + -6) Remove parenthesis around (11 + 8z) -1 + 1z = 11 + 8z + -1(3z + -6) Reorder the terms: -1 + 1z = 11 + 8z + -1(-6 + 3z) -1 + 1z = 11 + 8z + (-6 * -1 + 3z * -1) -1 + 1z = 11 + 8z + (6 + -3z) Reorder the terms: -1 + 1z = 11 + 6 + 8z + -3z Combine like terms: 11 + 6 = 17 -1 + 1z = 17 + 8z + -3z Combine like terms: 8z + -3z = 5z -1 + 1z = 17 + 5z Solving -1 + 1z = 17 + 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. -1 + 1z + -5z = 17 + 5z + -5z Combine like terms: 1z + -5z = -4z -1 + -4z = 17 + 5z + -5z Combine like terms: 5z + -5z = 0 -1 + -4z = 17 + 0 -1 + -4z = 17 Add '1' to each side of the equation. -1 + 1 + -4z = 17 + 1 Combine like terms: -1 + 1 = 0 0 + -4z = 17 + 1 -4z = 17 + 1 Combine like terms: 17 + 1 = 18 -4z = 18 Divide each side by '-4'. z = -4.5 Simplifying z = -4.5
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