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Simplifying 10(z + 3) + -3(z + -3) = 2(z + -1) + 4(z + -4) Reorder the terms: 10(3 + z) + -3(z + -3) = 2(z + -1) + 4(z + -4) (3 * 10 + z * 10) + -3(z + -3) = 2(z + -1) + 4(z + -4) (30 + 10z) + -3(z + -3) = 2(z + -1) + 4(z + -4) Reorder the terms: 30 + 10z + -3(-3 + z) = 2(z + -1) + 4(z + -4) 30 + 10z + (-3 * -3 + z * -3) = 2(z + -1) + 4(z + -4) 30 + 10z + (9 + -3z) = 2(z + -1) + 4(z + -4) Reorder the terms: 30 + 9 + 10z + -3z = 2(z + -1) + 4(z + -4) Combine like terms: 30 + 9 = 39 39 + 10z + -3z = 2(z + -1) + 4(z + -4) Combine like terms: 10z + -3z = 7z 39 + 7z = 2(z + -1) + 4(z + -4) Reorder the terms: 39 + 7z = 2(-1 + z) + 4(z + -4) 39 + 7z = (-1 * 2 + z * 2) + 4(z + -4) 39 + 7z = (-2 + 2z) + 4(z + -4) Reorder the terms: 39 + 7z = -2 + 2z + 4(-4 + z) 39 + 7z = -2 + 2z + (-4 * 4 + z * 4) 39 + 7z = -2 + 2z + (-16 + 4z) Reorder the terms: 39 + 7z = -2 + -16 + 2z + 4z Combine like terms: -2 + -16 = -18 39 + 7z = -18 + 2z + 4z Combine like terms: 2z + 4z = 6z 39 + 7z = -18 + 6z Solving 39 + 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. 39 + 7z + -6z = -18 + 6z + -6z Combine like terms: 7z + -6z = 1z 39 + 1z = -18 + 6z + -6z Combine like terms: 6z + -6z = 0 39 + 1z = -18 + 0 39 + 1z = -18 Add '-39' to each side of the equation. 39 + -39 + 1z = -18 + -39 Combine like terms: 39 + -39 = 0 0 + 1z = -18 + -39 1z = -18 + -39 Combine like terms: -18 + -39 = -57 1z = -57 Divide each side by '1'. z = -57 Simplifying z = -57
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