Questions: Solve for (x). [ frac7x=frac21x-5 ] Simplify your answer as much as possible. [ x= ]

Solve for (x). [ frac7x=frac21x-5 ] Simplify your answer as much as possible. [ x= ]
Transcript text: Solve for $x$. \[ \frac{7}{x}=\frac{21}{x}-5 \] Simplify your answer as much as possible. \[ x= \]
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Solution

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Solution Steps

To solve the given rational equation, we need to isolate the variable \( x \). Here are the high-level steps:

  1. Start by simplifying the equation by eliminating the fractions.
  2. Combine like terms to isolate \( x \).
  3. Solve for \( x \).
Step 1: Eliminate Fractions

We start with the equation: \[ \frac{7}{x} = \frac{21}{x} - 5 \] To eliminate the fractions, we can multiply both sides by \( x \) (assuming \( x \neq 0 \)): \[ 7 = 21 - 5x \]

Step 2: Rearrange the Equation

Next, we rearrange the equation to isolate the term involving \( x \): \[ 5x = 21 - 7 \] This simplifies to: \[ 5x = 14 \]

Step 3: Solve for \( x \)

Now, we divide both sides by 5 to solve for \( x \): \[ x = \frac{14}{5} \]

Final Answer

\[ \boxed{x = \frac{14}{5}} \]

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