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Simplifying 5(z + 3) + 9 = 3(z + -2) + 6 Reorder the terms: 5(3 + z) + 9 = 3(z + -2) + 6 (3 * 5 + z * 5) + 9 = 3(z + -2) + 6 (15 + 5z) + 9 = 3(z + -2) + 6 Reorder the terms: 15 + 9 + 5z = 3(z + -2) + 6 Combine like terms: 15 + 9 = 24 24 + 5z = 3(z + -2) + 6 Reorder the terms: 24 + 5z = 3(-2 + z) + 6 24 + 5z = (-2 * 3 + z * 3) + 6 24 + 5z = (-6 + 3z) + 6 Reorder the terms: 24 + 5z = -6 + 6 + 3z Combine like terms: -6 + 6 = 0 24 + 5z = 0 + 3z 24 + 5z = 3z Solving 24 + 5z = 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. 24 + 5z + -3z = 3z + -3z Combine like terms: 5z + -3z = 2z 24 + 2z = 3z + -3z Combine like terms: 3z + -3z = 0 24 + 2z = 0 Add '-24' to each side of the equation. 24 + -24 + 2z = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 2z = 0 + -24 2z = 0 + -24 Combine like terms: 0 + -24 = -24 2z = -24 Divide each side by '2'. z = -12 Simplifying z = -12
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