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Simplifying 4(4z + 4) + -16(z + 3) = -1z + -7(z + 8) Reorder the terms: 4(4 + 4z) + -16(z + 3) = -1z + -7(z + 8) (4 * 4 + 4z * 4) + -16(z + 3) = -1z + -7(z + 8) (16 + 16z) + -16(z + 3) = -1z + -7(z + 8) Reorder the terms: 16 + 16z + -16(3 + z) = -1z + -7(z + 8) 16 + 16z + (3 * -16 + z * -16) = -1z + -7(z + 8) 16 + 16z + (-48 + -16z) = -1z + -7(z + 8) Reorder the terms: 16 + -48 + 16z + -16z = -1z + -7(z + 8) Combine like terms: 16 + -48 = -32 -32 + 16z + -16z = -1z + -7(z + 8) Combine like terms: 16z + -16z = 0 -32 + 0 = -1z + -7(z + 8) -32 = -1z + -7(z + 8) Reorder the terms: -32 = -1z + -7(8 + z) -32 = -1z + (8 * -7 + z * -7) -32 = -1z + (-56 + -7z) Reorder the terms: -32 = -56 + -1z + -7z Combine like terms: -1z + -7z = -8z -32 = -56 + -8z Solving -32 = -56 + -8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8z' to each side of the equation. -32 + 8z = -56 + -8z + 8z Combine like terms: -8z + 8z = 0 -32 + 8z = -56 + 0 -32 + 8z = -56 Add '32' to each side of the equation. -32 + 32 + 8z = -56 + 32 Combine like terms: -32 + 32 = 0 0 + 8z = -56 + 32 8z = -56 + 32 Combine like terms: -56 + 32 = -24 8z = -24 Divide each side by '8'. z = -3 Simplifying z = -3
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