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Simplifying 3z + [-5z + -1(z + 3)] = 8z + (-5z + -9) Reorder the terms: 3z + [-5z + -1(3 + z)] = 8z + (-5z + -9) 3z + [-5z + (3 * -1 + z * -1)] = 8z + (-5z + -9) 3z + [-5z + (-3 + -1z)] = 8z + (-5z + -9) Reorder the terms: 3z + [-3 + -5z + -1z] = 8z + (-5z + -9) Combine like terms: -5z + -1z = -6z 3z + [-3 + -6z] = 8z + (-5z + -9) Remove brackets around [-3 + -6z] 3z + -3 + -6z = 8z + (-5z + -9) Reorder the terms: -3 + 3z + -6z = 8z + (-5z + -9) Combine like terms: 3z + -6z = -3z -3 + -3z = 8z + (-5z + -9) Reorder the terms: -3 + -3z = 8z + (-9 + -5z) Remove parenthesis around (-9 + -5z) -3 + -3z = 8z + -9 + -5z Reorder the terms: -3 + -3z = -9 + 8z + -5z Combine like terms: 8z + -5z = 3z -3 + -3z = -9 + 3z Solving -3 + -3z = -9 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -3 + -3z + -3z = -9 + 3z + -3z Combine like terms: -3z + -3z = -6z -3 + -6z = -9 + 3z + -3z Combine like terms: 3z + -3z = 0 -3 + -6z = -9 + 0 -3 + -6z = -9 Add '3' to each side of the equation. -3 + 3 + -6z = -9 + 3 Combine like terms: -3 + 3 = 0 0 + -6z = -9 + 3 -6z = -9 + 3 Combine like terms: -9 + 3 = -6 -6z = -6 Divide each side by '-6'. z = 1 Simplifying z = 1
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