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Simplifying 4(4z + 4) + -16(z + 3) = -1z + -1(z + 8) Reorder the terms: 4(4 + 4z) + -16(z + 3) = -1z + -1(z + 8) (4 * 4 + 4z * 4) + -16(z + 3) = -1z + -1(z + 8) (16 + 16z) + -16(z + 3) = -1z + -1(z + 8) Reorder the terms: 16 + 16z + -16(3 + z) = -1z + -1(z + 8) 16 + 16z + (3 * -16 + z * -16) = -1z + -1(z + 8) 16 + 16z + (-48 + -16z) = -1z + -1(z + 8) Reorder the terms: 16 + -48 + 16z + -16z = -1z + -1(z + 8) Combine like terms: 16 + -48 = -32 -32 + 16z + -16z = -1z + -1(z + 8) Combine like terms: 16z + -16z = 0 -32 + 0 = -1z + -1(z + 8) -32 = -1z + -1(z + 8) Reorder the terms: -32 = -1z + -1(8 + z) -32 = -1z + (8 * -1 + z * -1) -32 = -1z + (-8 + -1z) Reorder the terms: -32 = -8 + -1z + -1z Combine like terms: -1z + -1z = -2z -32 = -8 + -2z Solving -32 = -8 + -2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2z' to each side of the equation. -32 + 2z = -8 + -2z + 2z Combine like terms: -2z + 2z = 0 -32 + 2z = -8 + 0 -32 + 2z = -8 Add '32' to each side of the equation. -32 + 32 + 2z = -8 + 32 Combine like terms: -32 + 32 = 0 0 + 2z = -8 + 32 2z = -8 + 32 Combine like terms: -8 + 32 = 24 2z = 24 Divide each side by '2'. z = 12 Simplifying z = 12
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