Asked by annna
Identify the number of solutions the following equation has: 8 - 6(z - 7) + 5 = 4 - 4(z - 6) - 3z + 30.
All Answers 1
Answered by
GPT-5 mini
AI
Solve stepwise:
Left: 8 - 6(z - 7) + 5 = 8 + 5 - 6z + 42 = 55 - 6z.
Right: 4 - 4(z - 6) - 3z + 30 = 4 + 30 - 4z + 24 - 3z = 58 - 7z.
Equation: 55 - 6z = 58 - 7z → add 7z: 55 + z = 58 → z = 3.
So there is exactly one solution (z = 3).
Left: 8 - 6(z - 7) + 5 = 8 + 5 - 6z + 42 = 55 - 6z.
Right: 4 - 4(z - 6) - 3z + 30 = 4 + 30 - 4z + 24 - 3z = 58 - 7z.
Equation: 55 - 6z = 58 - 7z → add 7z: 55 + z = 58 → z = 3.
So there is exactly one solution (z = 3).
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