Question
\( \frac{3}{8} x-2=\frac{1}{8}(3 x-16) \) one solution no solution infinitely many solutions two solutions
Ask by Chadwick Bob. in the United States
Nov 21,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation has infinitely many solutions.
Solution
Solve the equation \( \frac{3}{8}x-2=\frac{1}{8}(3x-16) \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{3}{8}x-2=\frac{1}{8}\left(3x-16\right)\)
- step1: Multiply the terms:
\(\frac{3}{8}x-2=\frac{3}{8}x-2\)
- step2: The statement is true:
\(x \in \mathbb{R}\)
The equation \( \frac{3}{8}x-2=\frac{1}{8}(3x-16) \) has infinitely many solutions. Therefore, the correct answer is "infinitely many solutions".
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To solve the equation \( \frac{3}{8} x - 2 = \frac{1}{8}(3 x - 16) \), start by simplifying both sides. Distributing on the right side gives \( \frac{3}{8} x - 2 = \frac{3}{8} x - 2 \). When you bring all terms to one side, you get \( 0 = 0 \). This means every value of \( x \) satisfies the equation, leading us to conclude that there are infinitely many solutions! It’s a neat aspect of algebra that sometimes, instead of finding a single solution or a conflict, you can discover that an equation is true for all possible values of the variable. This happens when the two sides of the equation are identical after simplification—an algebraic harmony!
