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Simplifying 8[z + -1(8z + 56) + 7] = 4(z + 7) Reorder the terms: 8[z + -1(56 + 8z) + 7] = 4(z + 7) 8[z + (56 * -1 + 8z * -1) + 7] = 4(z + 7) 8[z + (-56 + -8z) + 7] = 4(z + 7) Reorder the terms: 8[-56 + 7 + z + -8z] = 4(z + 7) Combine like terms: -56 + 7 = -49 8[-49 + z + -8z] = 4(z + 7) Combine like terms: z + -8z = -7z 8[-49 + -7z] = 4(z + 7) [-49 * 8 + -7z * 8] = 4(z + 7) [-392 + -56z] = 4(z + 7) Reorder the terms: -392 + -56z = 4(7 + z) -392 + -56z = (7 * 4 + z * 4) -392 + -56z = (28 + 4z) Solving -392 + -56z = 28 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -392 + -56z + -4z = 28 + 4z + -4z Combine like terms: -56z + -4z = -60z -392 + -60z = 28 + 4z + -4z Combine like terms: 4z + -4z = 0 -392 + -60z = 28 + 0 -392 + -60z = 28 Add '392' to each side of the equation. -392 + 392 + -60z = 28 + 392 Combine like terms: -392 + 392 = 0 0 + -60z = 28 + 392 -60z = 28 + 392 Combine like terms: 28 + 392 = 420 -60z = 420 Divide each side by '-60'. z = -7 Simplifying z = -7
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