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Simplifying 10(z + 1) + -2(z + -4) = 4(z + -4) + 3(z + -2) Reorder the terms: 10(1 + z) + -2(z + -4) = 4(z + -4) + 3(z + -2) (1 * 10 + z * 10) + -2(z + -4) = 4(z + -4) + 3(z + -2) (10 + 10z) + -2(z + -4) = 4(z + -4) + 3(z + -2) Reorder the terms: 10 + 10z + -2(-4 + z) = 4(z + -4) + 3(z + -2) 10 + 10z + (-4 * -2 + z * -2) = 4(z + -4) + 3(z + -2) 10 + 10z + (8 + -2z) = 4(z + -4) + 3(z + -2) Reorder the terms: 10 + 8 + 10z + -2z = 4(z + -4) + 3(z + -2) Combine like terms: 10 + 8 = 18 18 + 10z + -2z = 4(z + -4) + 3(z + -2) Combine like terms: 10z + -2z = 8z 18 + 8z = 4(z + -4) + 3(z + -2) Reorder the terms: 18 + 8z = 4(-4 + z) + 3(z + -2) 18 + 8z = (-4 * 4 + z * 4) + 3(z + -2) 18 + 8z = (-16 + 4z) + 3(z + -2) Reorder the terms: 18 + 8z = -16 + 4z + 3(-2 + z) 18 + 8z = -16 + 4z + (-2 * 3 + z * 3) 18 + 8z = -16 + 4z + (-6 + 3z) Reorder the terms: 18 + 8z = -16 + -6 + 4z + 3z Combine like terms: -16 + -6 = -22 18 + 8z = -22 + 4z + 3z Combine like terms: 4z + 3z = 7z 18 + 8z = -22 + 7z Solving 18 + 8z = -22 + 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. 18 + 8z + -7z = -22 + 7z + -7z Combine like terms: 8z + -7z = 1z 18 + 1z = -22 + 7z + -7z Combine like terms: 7z + -7z = 0 18 + 1z = -22 + 0 18 + 1z = -22 Add '-18' to each side of the equation. 18 + -18 + 1z = -22 + -18 Combine like terms: 18 + -18 = 0 0 + 1z = -22 + -18 1z = -22 + -18 Combine like terms: -22 + -18 = -40 1z = -40 Divide each side by '1'. z = -40 Simplifying z = -40
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