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Simplifying 11(z + 1) + -3(z + -2) = 4(z + -1) + 3(z + -4) Reorder the terms: 11(1 + z) + -3(z + -2) = 4(z + -1) + 3(z + -4) (1 * 11 + z * 11) + -3(z + -2) = 4(z + -1) + 3(z + -4) (11 + 11z) + -3(z + -2) = 4(z + -1) + 3(z + -4) Reorder the terms: 11 + 11z + -3(-2 + z) = 4(z + -1) + 3(z + -4) 11 + 11z + (-2 * -3 + z * -3) = 4(z + -1) + 3(z + -4) 11 + 11z + (6 + -3z) = 4(z + -1) + 3(z + -4) Reorder the terms: 11 + 6 + 11z + -3z = 4(z + -1) + 3(z + -4) Combine like terms: 11 + 6 = 17 17 + 11z + -3z = 4(z + -1) + 3(z + -4) Combine like terms: 11z + -3z = 8z 17 + 8z = 4(z + -1) + 3(z + -4) Reorder the terms: 17 + 8z = 4(-1 + z) + 3(z + -4) 17 + 8z = (-1 * 4 + z * 4) + 3(z + -4) 17 + 8z = (-4 + 4z) + 3(z + -4) Reorder the terms: 17 + 8z = -4 + 4z + 3(-4 + z) 17 + 8z = -4 + 4z + (-4 * 3 + z * 3) 17 + 8z = -4 + 4z + (-12 + 3z) Reorder the terms: 17 + 8z = -4 + -12 + 4z + 3z Combine like terms: -4 + -12 = -16 17 + 8z = -16 + 4z + 3z Combine like terms: 4z + 3z = 7z 17 + 8z = -16 + 7z Solving 17 + 8z = -16 + 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. 17 + 8z + -7z = -16 + 7z + -7z Combine like terms: 8z + -7z = 1z 17 + 1z = -16 + 7z + -7z Combine like terms: 7z + -7z = 0 17 + 1z = -16 + 0 17 + 1z = -16 Add '-17' to each side of the equation. 17 + -17 + 1z = -16 + -17 Combine like terms: 17 + -17 = 0 0 + 1z = -16 + -17 1z = -16 + -17 Combine like terms: -16 + -17 = -33 1z = -33 Divide each side by '1'. z = -33 Simplifying z = -33
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