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Simplifying 6(z + 3) + -5(3z + 2) = 2(z + -9) Reorder the terms: 6(3 + z) + -5(3z + 2) = 2(z + -9) (3 * 6 + z * 6) + -5(3z + 2) = 2(z + -9) (18 + 6z) + -5(3z + 2) = 2(z + -9) Reorder the terms: 18 + 6z + -5(2 + 3z) = 2(z + -9) 18 + 6z + (2 * -5 + 3z * -5) = 2(z + -9) 18 + 6z + (-10 + -15z) = 2(z + -9) Reorder the terms: 18 + -10 + 6z + -15z = 2(z + -9) Combine like terms: 18 + -10 = 8 8 + 6z + -15z = 2(z + -9) Combine like terms: 6z + -15z = -9z 8 + -9z = 2(z + -9) Reorder the terms: 8 + -9z = 2(-9 + z) 8 + -9z = (-9 * 2 + z * 2) 8 + -9z = (-18 + 2z) Solving 8 + -9z = -18 + 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. 8 + -9z + -2z = -18 + 2z + -2z Combine like terms: -9z + -2z = -11z 8 + -11z = -18 + 2z + -2z Combine like terms: 2z + -2z = 0 8 + -11z = -18 + 0 8 + -11z = -18 Add '-8' to each side of the equation. 8 + -8 + -11z = -18 + -8 Combine like terms: 8 + -8 = 0 0 + -11z = -18 + -8 -11z = -18 + -8 Combine like terms: -18 + -8 = -26 -11z = -26 Divide each side by '-11'. z = 2.363636364 Simplifying z = 2.363636364
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