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Simplifying 10z + 10(4) + -4z + -4(2) = 3z + -3(1) + 2z + -2(3) Multiply 10 * 4 10z + 40 + -4z + -4(2) = 3z + -3(1) + 2z + -2(3) Multiply -4 * 2 10z + 40 + -4z + -8 = 3z + -3(1) + 2z + -2(3) Reorder the terms: 40 + -8 + 10z + -4z = 3z + -3(1) + 2z + -2(3) Combine like terms: 40 + -8 = 32 32 + 10z + -4z = 3z + -3(1) + 2z + -2(3) Combine like terms: 10z + -4z = 6z 32 + 6z = 3z + -3(1) + 2z + -2(3) Multiply -3 * 1 32 + 6z = 3z + -3 + 2z + -2(3) Multiply -2 * 3 32 + 6z = 3z + -3 + 2z + -6 Reorder the terms: 32 + 6z = -3 + -6 + 3z + 2z Combine like terms: -3 + -6 = -9 32 + 6z = -9 + 3z + 2z Combine like terms: 3z + 2z = 5z 32 + 6z = -9 + 5z Solving 32 + 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. 32 + 6z + -5z = -9 + 5z + -5z Combine like terms: 6z + -5z = 1z 32 + 1z = -9 + 5z + -5z Combine like terms: 5z + -5z = 0 32 + 1z = -9 + 0 32 + 1z = -9 Add '-32' to each side of the equation. 32 + -32 + 1z = -9 + -32 Combine like terms: 32 + -32 = 0 0 + 1z = -9 + -32 1z = -9 + -32 Combine like terms: -9 + -32 = -41 1z = -41 Divide each side by '1'. z = -41 Simplifying z = -41
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