Question
Solve for \( x \) in this equation: \( |2.5 x-6.8|=12.9 \) Step 1. Rewrite the absolute value equation as two linear equations Negative case: Positive case
Ask by Jimenez Barker. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( x = -2.44 \) and \( x = 7.88 \).
Solution
Solve the equation \( |2.5x-6.8|=12.9 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\left|2.5x-6.8\right|=12.9\)
- step1: Simplify:
\(\left|\frac{5}{2}x-\frac{34}{5}\right|=12.9\)
- step2: Calculate:
\(\left|\frac{5}{2}x-\frac{34}{5}\right|=\frac{129}{10}\)
- step3: Separate into possible cases:
\(\begin{align}&\frac{5}{2}x-\frac{34}{5}=\frac{129}{10}\\&\frac{5}{2}x-\frac{34}{5}=-\frac{129}{10}\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=\frac{197}{25}\\&x=-\frac{61}{25}\end{align}\)
- step5: Rewrite:
\(x_{1}=-\frac{61}{25},x_{2}=\frac{197}{25}\)
The solutions to the equation \(|2.5x-6.8|=12.9\) are \(x=-2.44\) and \(x=7.88\).
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To solve the absolute value equation \( |2.5x - 6.8| = 12.9 \), we can split it into two cases based on the definition of absolute value. For the **negative case**, we set up the equation \( 2.5x - 6.8 = -12.9 \). For the **positive case**, we set up the equation \( 2.5x - 6.8 = 12.9 \). Now you're ready to solve each linear equation for \( x \)! Just remember that when working with absolute values, it’s important to consider both scenarios to find all possible solutions.
