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Simplifying 10(z + 1) + -2(z + -2) = 3(z + -2) + 4(z + -3) Reorder the terms: 10(1 + z) + -2(z + -2) = 3(z + -2) + 4(z + -3) (1 * 10 + z * 10) + -2(z + -2) = 3(z + -2) + 4(z + -3) (10 + 10z) + -2(z + -2) = 3(z + -2) + 4(z + -3) Reorder the terms: 10 + 10z + -2(-2 + z) = 3(z + -2) + 4(z + -3) 10 + 10z + (-2 * -2 + z * -2) = 3(z + -2) + 4(z + -3) 10 + 10z + (4 + -2z) = 3(z + -2) + 4(z + -3) Reorder the terms: 10 + 4 + 10z + -2z = 3(z + -2) + 4(z + -3) Combine like terms: 10 + 4 = 14 14 + 10z + -2z = 3(z + -2) + 4(z + -3) Combine like terms: 10z + -2z = 8z 14 + 8z = 3(z + -2) + 4(z + -3) Reorder the terms: 14 + 8z = 3(-2 + z) + 4(z + -3) 14 + 8z = (-2 * 3 + z * 3) + 4(z + -3) 14 + 8z = (-6 + 3z) + 4(z + -3) Reorder the terms: 14 + 8z = -6 + 3z + 4(-3 + z) 14 + 8z = -6 + 3z + (-3 * 4 + z * 4) 14 + 8z = -6 + 3z + (-12 + 4z) Reorder the terms: 14 + 8z = -6 + -12 + 3z + 4z Combine like terms: -6 + -12 = -18 14 + 8z = -18 + 3z + 4z Combine like terms: 3z + 4z = 7z 14 + 8z = -18 + 7z Solving 14 + 8z = -18 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. 14 + 8z + -7z = -18 + 7z + -7z Combine like terms: 8z + -7z = 1z 14 + 1z = -18 + 7z + -7z Combine like terms: 7z + -7z = 0 14 + 1z = -18 + 0 14 + 1z = -18 Add '-14' to each side of the equation. 14 + -14 + 1z = -18 + -14 Combine like terms: 14 + -14 = 0 0 + 1z = -18 + -14 1z = -18 + -14 Combine like terms: -18 + -14 = -32 1z = -32 Divide each side by '1'. z = -32 Simplifying z = -32
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