Pregunta
Solve the absolute equation \[ \begin{array}{l}|2 x-4|=10 \\ \text { a) } x=-3, x=7 \\ \text { b) } x=-7, x=3 \\ \text { c) } x=7 \\ \text { d) } x=-2, x=6\end{array} \]
Ask by Barrett Thornton. in the United States
Feb 21,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The solutions are \(x=-3\) and \(x=7\).
Solución
Solve the equation \( |2x-4|=10 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\left|2x-4\right|=10\)
- step1: Separate into possible cases:
\(\begin{align}&2x-4=10\\&2x-4=-10\end{align}\)
- step2: Solve the equation:
\(\begin{align}&x=7\\&x=-3\end{align}\)
- step3: Rewrite:
\(x_{1}=-3,x_{2}=7\)
The solutions to the absolute equation \(|2x-4|=10\) are \(x=-3\) and \(x=7\).
Therefore, the correct answer is:
a) \(x=-3, x=7\)
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Simplifique esta solución The Deep Dive
To solve the absolute value equation \( |2x - 4| = 10 \), we need to set up two separate equations based on the definition of absolute value. 1. \( 2x - 4 = 10 \) 2. \( 2x - 4 = -10 \) For the first equation: \[ 2x - 4 = 10 \\ 2x = 10 + 4 \\ 2x = 14 \\ x = 7 \] For the second equation: \[ 2x - 4 = -10 \\ 2x = -10 + 4 \\ 2x = -6 \\ x = -3 \] Thus, the solutions to the equation \( |2x - 4| = 10 \) are \( x = 7 \) and \( x = -3 \). So the correct answer is: **a) \( x = -3, x = 7 \)**.
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