Question
How many solutions does the following equation have? \( -9(z+8)=-9 z-72 \) Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions
Ask by Welch Franklin. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are infinitely many solutions.
Solution
We start by distributing and simplifying the equation:
-9(z + 8) = -9z - 72
which becomes
-9z - 72 = -9z - 72.
Since both sides are exactly the same, this equation holds for any value of z. Therefore, there are infinitely many solutions.
Answer: (C) Infinitely many solutions.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To determine the number of solutions, let's first simplify the equation: Starting with \( -9(z + 8) = -9z - 72 \), we distribute the left side to get: \(-9z - 72 = -9z - 72\). Now observe that both sides are identical. This means that the equation holds true for any value of \( z \). Thus, there are infinitely many solutions to the equation. So the correct answer is (C) Infinitely many solutions.
