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Simplifying 10(z + 2) + -3(z + -4) = 4(z + -2) + 2(z + -2) Reorder the terms: 10(2 + z) + -3(z + -4) = 4(z + -2) + 2(z + -2) (2 * 10 + z * 10) + -3(z + -4) = 4(z + -2) + 2(z + -2) (20 + 10z) + -3(z + -4) = 4(z + -2) + 2(z + -2) Reorder the terms: 20 + 10z + -3(-4 + z) = 4(z + -2) + 2(z + -2) 20 + 10z + (-4 * -3 + z * -3) = 4(z + -2) + 2(z + -2) 20 + 10z + (12 + -3z) = 4(z + -2) + 2(z + -2) Reorder the terms: 20 + 12 + 10z + -3z = 4(z + -2) + 2(z + -2) Combine like terms: 20 + 12 = 32 32 + 10z + -3z = 4(z + -2) + 2(z + -2) Combine like terms: 10z + -3z = 7z 32 + 7z = 4(z + -2) + 2(z + -2) Reorder the terms: 32 + 7z = 4(-2 + z) + 2(z + -2) 32 + 7z = (-2 * 4 + z * 4) + 2(z + -2) 32 + 7z = (-8 + 4z) + 2(z + -2) Reorder the terms: 32 + 7z = -8 + 4z + 2(-2 + z) 32 + 7z = -8 + 4z + (-2 * 2 + z * 2) 32 + 7z = -8 + 4z + (-4 + 2z) Reorder the terms: 32 + 7z = -8 + -4 + 4z + 2z Combine like terms: -8 + -4 = -12 32 + 7z = -12 + 4z + 2z Combine like terms: 4z + 2z = 6z 32 + 7z = -12 + 6z Solving 32 + 7z = -12 + 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. 32 + 7z + -6z = -12 + 6z + -6z Combine like terms: 7z + -6z = 1z 32 + 1z = -12 + 6z + -6z Combine like terms: 6z + -6z = 0 32 + 1z = -12 + 0 32 + 1z = -12 Add '-32' to each side of the equation. 32 + -32 + 1z = -12 + -32 Combine like terms: 32 + -32 = 0 0 + 1z = -12 + -32 1z = -12 + -32 Combine like terms: -12 + -32 = -44 1z = -44 Divide each side by '1'. z = -44 Simplifying z = -44
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