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Simplifying 10(z + 1) + -3(z + -2) = 2(z + -3) + 4(z + -3) Reorder the terms: 10(1 + z) + -3(z + -2) = 2(z + -3) + 4(z + -3) (1 * 10 + z * 10) + -3(z + -2) = 2(z + -3) + 4(z + -3) (10 + 10z) + -3(z + -2) = 2(z + -3) + 4(z + -3) Reorder the terms: 10 + 10z + -3(-2 + z) = 2(z + -3) + 4(z + -3) 10 + 10z + (-2 * -3 + z * -3) = 2(z + -3) + 4(z + -3) 10 + 10z + (6 + -3z) = 2(z + -3) + 4(z + -3) Reorder the terms: 10 + 6 + 10z + -3z = 2(z + -3) + 4(z + -3) Combine like terms: 10 + 6 = 16 16 + 10z + -3z = 2(z + -3) + 4(z + -3) Combine like terms: 10z + -3z = 7z 16 + 7z = 2(z + -3) + 4(z + -3) Reorder the terms: 16 + 7z = 2(-3 + z) + 4(z + -3) 16 + 7z = (-3 * 2 + z * 2) + 4(z + -3) 16 + 7z = (-6 + 2z) + 4(z + -3) Reorder the terms: 16 + 7z = -6 + 2z + 4(-3 + z) 16 + 7z = -6 + 2z + (-3 * 4 + z * 4) 16 + 7z = -6 + 2z + (-12 + 4z) Reorder the terms: 16 + 7z = -6 + -12 + 2z + 4z Combine like terms: -6 + -12 = -18 16 + 7z = -18 + 2z + 4z Combine like terms: 2z + 4z = 6z 16 + 7z = -18 + 6z Solving 16 + 7z = -18 + 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. 16 + 7z + -6z = -18 + 6z + -6z Combine like terms: 7z + -6z = 1z 16 + 1z = -18 + 6z + -6z Combine like terms: 6z + -6z = 0 16 + 1z = -18 + 0 16 + 1z = -18 Add '-16' to each side of the equation. 16 + -16 + 1z = -18 + -16 Combine like terms: 16 + -16 = 0 0 + 1z = -18 + -16 1z = -18 + -16 Combine like terms: -18 + -16 = -34 1z = -34 Divide each side by '1'. z = -34 Simplifying z = -34
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