Question
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Answer
The solutions are \( x=2.5 \) and \( x=4.5 \).
Solution
Solve the equation \( |2x-7|=2 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\left|2x-7\right|=2\)
- step1: Separate into possible cases:
\(\begin{align}&2x-7=2\\&2x-7=-2\end{align}\)
- step2: Solve the equation:
\(\begin{align}&x=\frac{9}{2}\\&x=\frac{5}{2}\end{align}\)
- step3: Rewrite:
\(x_{1}=\frac{5}{2},x_{2}=\frac{9}{2}\)
The solutions to the equation \(|2x-7|=2\) are \(x=\frac{5}{2}\) and \(x=\frac{9}{2}\), which can also be written as \(x=2.5\) and \(x=4.5\).
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Simplify this solution Extra Insights
To solve \( |2x - 7| = 2 \), we must consider two cases. The first case is when the expression inside the absolute value is equal to \( 2 \): 1. \( 2x - 7 = 2 \) Solving this gives \( 2x = 9 \) and \( x = 4.5 \). The second case is when the expression inside the absolute value is equal to \( -2 \): 2. \( 2x - 7 = -2 \) Solving this gives \( 2x = 5 \) and \( x = 2.5 \). Therefore, the solutions are \( x = 4.5 \) and \( x = 2.5 \).
