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Simplifying 10(z + 2) + -4(z + -2) = 3(z + -3) + 2(z + -2) Reorder the terms: 10(2 + z) + -4(z + -2) = 3(z + -3) + 2(z + -2) (2 * 10 + z * 10) + -4(z + -2) = 3(z + -3) + 2(z + -2) (20 + 10z) + -4(z + -2) = 3(z + -3) + 2(z + -2) Reorder the terms: 20 + 10z + -4(-2 + z) = 3(z + -3) + 2(z + -2) 20 + 10z + (-2 * -4 + z * -4) = 3(z + -3) + 2(z + -2) 20 + 10z + (8 + -4z) = 3(z + -3) + 2(z + -2) Reorder the terms: 20 + 8 + 10z + -4z = 3(z + -3) + 2(z + -2) Combine like terms: 20 + 8 = 28 28 + 10z + -4z = 3(z + -3) + 2(z + -2) Combine like terms: 10z + -4z = 6z 28 + 6z = 3(z + -3) + 2(z + -2) Reorder the terms: 28 + 6z = 3(-3 + z) + 2(z + -2) 28 + 6z = (-3 * 3 + z * 3) + 2(z + -2) 28 + 6z = (-9 + 3z) + 2(z + -2) Reorder the terms: 28 + 6z = -9 + 3z + 2(-2 + z) 28 + 6z = -9 + 3z + (-2 * 2 + z * 2) 28 + 6z = -9 + 3z + (-4 + 2z) Reorder the terms: 28 + 6z = -9 + -4 + 3z + 2z Combine like terms: -9 + -4 = -13 28 + 6z = -13 + 3z + 2z Combine like terms: 3z + 2z = 5z 28 + 6z = -13 + 5z Solving 28 + 6z = -13 + 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. 28 + 6z + -5z = -13 + 5z + -5z Combine like terms: 6z + -5z = 1z 28 + 1z = -13 + 5z + -5z Combine like terms: 5z + -5z = 0 28 + 1z = -13 + 0 28 + 1z = -13 Add '-28' to each side of the equation. 28 + -28 + 1z = -13 + -28 Combine like terms: 28 + -28 = 0 0 + 1z = -13 + -28 1z = -13 + -28 Combine like terms: -13 + -28 = -41 1z = -41 Divide each side by '1'. z = -41 Simplifying z = -41
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