Question
\begin{tabular}{l} Solve for \( x \) \\ \( \qquad=\frac{x+37}{7} \) \\ Simplify your answer as much as possible. \\ \( x=\square \) \\ \( \frac{\square}{\square} \) \\ \hline\end{tabular}
Ask by Deleon Mann. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \frac{37}{6} \)
Solution
Solve the equation \( x=\frac{x+37}{7} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(x=\frac{x+37}{7}\)
- step1: Cross multiply:
\(x\times 7=x+37\)
- step2: Simplify the equation:
\(7x=x+37\)
- step3: Move the variable to the left side:
\(7x-x=37\)
- step4: Subtract the terms:
\(6x=37\)
- step5: Divide both sides:
\(\frac{6x}{6}=\frac{37}{6}\)
- step6: Divide the numbers:
\(x=\frac{37}{6}\)
The solution to the equation \( x = \frac{x+37}{7} \) is \( x = \frac{37}{6} \) or \( x = 6.166... \)
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Simplify this solution Extra Insights
To solve the equation \( x = \frac{x + 37}{7} \), we first eliminate the fraction by multiplying both sides by 7: \[ 7x = x + 37 \] Next, we isolate \( x \) by subtracting \( x \) from both sides: \[ 7x - x = 37 \implies 6x = 37 \] Now we divide both sides by 6 to solve for \( x \): \[ x = \frac{37}{6} \] So, we have \( x=\frac{37}{6} \). This means that the answer can be presented as: \( x=\frac{37}{6} \) In the simplified format: \( \frac{37}{6} = \frac{37}{6} \)
