Question
How many solutions does the following equation have? \( 4(y-30)=4 y+12 \) Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions
Ask by Moran Schneider. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are no solutions.
Solution
First, distribute the 4 on the left-hand side:
4y - 120 = 4y + 12
Next, subtract 4y from both sides:
4y - 4y - 120 = 4y - 4y + 12
-120 = 12
Since -120 does not equal 12, the equation is inconsistent. Therefore, there are no solutions.
Answer: (A) No solutions.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To solve the equation \( 4(y-30) = 4y + 12 \), first, distribute the 4 on the left side: \( 4y - 120 = 4y + 12 \). Next, subtract \( 4y \) from both sides: \( -120 = 12 \). Since this statement is obviously false, it indicates there are no values of \( y \) that can make the equation true. Therefore, the equation has (A) No solutions. Writing equations like this can often lead to false leads. A common mistake is to overlook the coefficients and focus solely on terms. One tip to avoid confusion is to simplify each side thoroughly before making comparisons, ensuring you don't jump to conclusions that can steer you away from the actual solution!
