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Simplifying 10(z + 40) + -4(z + -2) = 3(z + -1) + 2(z + -3) Reorder the terms: 10(40 + z) + -4(z + -2) = 3(z + -1) + 2(z + -3) (40 * 10 + z * 10) + -4(z + -2) = 3(z + -1) + 2(z + -3) (400 + 10z) + -4(z + -2) = 3(z + -1) + 2(z + -3) Reorder the terms: 400 + 10z + -4(-2 + z) = 3(z + -1) + 2(z + -3) 400 + 10z + (-2 * -4 + z * -4) = 3(z + -1) + 2(z + -3) 400 + 10z + (8 + -4z) = 3(z + -1) + 2(z + -3) Reorder the terms: 400 + 8 + 10z + -4z = 3(z + -1) + 2(z + -3) Combine like terms: 400 + 8 = 408 408 + 10z + -4z = 3(z + -1) + 2(z + -3) Combine like terms: 10z + -4z = 6z 408 + 6z = 3(z + -1) + 2(z + -3) Reorder the terms: 408 + 6z = 3(-1 + z) + 2(z + -3) 408 + 6z = (-1 * 3 + z * 3) + 2(z + -3) 408 + 6z = (-3 + 3z) + 2(z + -3) Reorder the terms: 408 + 6z = -3 + 3z + 2(-3 + z) 408 + 6z = -3 + 3z + (-3 * 2 + z * 2) 408 + 6z = -3 + 3z + (-6 + 2z) Reorder the terms: 408 + 6z = -3 + -6 + 3z + 2z Combine like terms: -3 + -6 = -9 408 + 6z = -9 + 3z + 2z Combine like terms: 3z + 2z = 5z 408 + 6z = -9 + 5z Solving 408 + 6z = -9 + 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. 408 + 6z + -5z = -9 + 5z + -5z Combine like terms: 6z + -5z = 1z 408 + 1z = -9 + 5z + -5z Combine like terms: 5z + -5z = 0 408 + 1z = -9 + 0 408 + 1z = -9 Add '-408' to each side of the equation. 408 + -408 + 1z = -9 + -408 Combine like terms: 408 + -408 = 0 0 + 1z = -9 + -408 1z = -9 + -408 Combine like terms: -9 + -408 = -417 1z = -417 Divide each side by '1'. z = -417 Simplifying z = -417
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