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Simplifying 9(z + 3) + -2(z + -4) = 2(z + -4) + 4(z + -3) Reorder the terms: 9(3 + z) + -2(z + -4) = 2(z + -4) + 4(z + -3) (3 * 9 + z * 9) + -2(z + -4) = 2(z + -4) + 4(z + -3) (27 + 9z) + -2(z + -4) = 2(z + -4) + 4(z + -3) Reorder the terms: 27 + 9z + -2(-4 + z) = 2(z + -4) + 4(z + -3) 27 + 9z + (-4 * -2 + z * -2) = 2(z + -4) + 4(z + -3) 27 + 9z + (8 + -2z) = 2(z + -4) + 4(z + -3) Reorder the terms: 27 + 8 + 9z + -2z = 2(z + -4) + 4(z + -3) Combine like terms: 27 + 8 = 35 35 + 9z + -2z = 2(z + -4) + 4(z + -3) Combine like terms: 9z + -2z = 7z 35 + 7z = 2(z + -4) + 4(z + -3) Reorder the terms: 35 + 7z = 2(-4 + z) + 4(z + -3) 35 + 7z = (-4 * 2 + z * 2) + 4(z + -3) 35 + 7z = (-8 + 2z) + 4(z + -3) Reorder the terms: 35 + 7z = -8 + 2z + 4(-3 + z) 35 + 7z = -8 + 2z + (-3 * 4 + z * 4) 35 + 7z = -8 + 2z + (-12 + 4z) Reorder the terms: 35 + 7z = -8 + -12 + 2z + 4z Combine like terms: -8 + -12 = -20 35 + 7z = -20 + 2z + 4z Combine like terms: 2z + 4z = 6z 35 + 7z = -20 + 6z Solving 35 + 7z = -20 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. 35 + 7z + -6z = -20 + 6z + -6z Combine like terms: 7z + -6z = 1z 35 + 1z = -20 + 6z + -6z Combine like terms: 6z + -6z = 0 35 + 1z = -20 + 0 35 + 1z = -20 Add '-35' to each side of the equation. 35 + -35 + 1z = -20 + -35 Combine like terms: 35 + -35 = 0 0 + 1z = -20 + -35 1z = -20 + -35 Combine like terms: -20 + -35 = -55 1z = -55 Divide each side by '1'. z = -55 Simplifying z = -55
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