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Simplifying 11(z + 4) + -3(z + -1) = 3(z + -4) + 4(z + -3) Reorder the terms: 11(4 + z) + -3(z + -1) = 3(z + -4) + 4(z + -3) (4 * 11 + z * 11) + -3(z + -1) = 3(z + -4) + 4(z + -3) (44 + 11z) + -3(z + -1) = 3(z + -4) + 4(z + -3) Reorder the terms: 44 + 11z + -3(-1 + z) = 3(z + -4) + 4(z + -3) 44 + 11z + (-1 * -3 + z * -3) = 3(z + -4) + 4(z + -3) 44 + 11z + (3 + -3z) = 3(z + -4) + 4(z + -3) Reorder the terms: 44 + 3 + 11z + -3z = 3(z + -4) + 4(z + -3) Combine like terms: 44 + 3 = 47 47 + 11z + -3z = 3(z + -4) + 4(z + -3) Combine like terms: 11z + -3z = 8z 47 + 8z = 3(z + -4) + 4(z + -3) Reorder the terms: 47 + 8z = 3(-4 + z) + 4(z + -3) 47 + 8z = (-4 * 3 + z * 3) + 4(z + -3) 47 + 8z = (-12 + 3z) + 4(z + -3) Reorder the terms: 47 + 8z = -12 + 3z + 4(-3 + z) 47 + 8z = -12 + 3z + (-3 * 4 + z * 4) 47 + 8z = -12 + 3z + (-12 + 4z) Reorder the terms: 47 + 8z = -12 + -12 + 3z + 4z Combine like terms: -12 + -12 = -24 47 + 8z = -24 + 3z + 4z Combine like terms: 3z + 4z = 7z 47 + 8z = -24 + 7z Solving 47 + 8z = -24 + 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. 47 + 8z + -7z = -24 + 7z + -7z Combine like terms: 8z + -7z = 1z 47 + 1z = -24 + 7z + -7z Combine like terms: 7z + -7z = 0 47 + 1z = -24 + 0 47 + 1z = -24 Add '-47' to each side of the equation. 47 + -47 + 1z = -24 + -47 Combine like terms: 47 + -47 = 0 0 + 1z = -24 + -47 1z = -24 + -47 Combine like terms: -24 + -47 = -71 1z = -71 Divide each side by '1'. z = -71 Simplifying z = -71
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