Questions: x/2 + x/7 = 9

x/2 + x/7 = 9
Transcript text: $\frac{x}{2}+\frac{x}{7}=9$
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Solution

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Solution Steps

To solve the equation \(\frac{x}{2} + \frac{x}{7} = 9\), we need to find a common denominator for the fractions on the left side. The common denominator of 2 and 7 is 14. Rewrite each fraction with this common denominator, combine them, and then solve for \(x\).

Step 1: Find a Common Denominator

To solve the equation \(\frac{x}{2} + \frac{x}{7} = 9\), we first find a common denominator for the fractions. The least common denominator of 2 and 7 is 14.

Step 2: Rewrite the Equation

Rewrite each fraction with the common denominator: \[ \frac{7x}{14} + \frac{2x}{14} = 9 \]

Step 3: Combine the Fractions

Combine the fractions on the left side: \[ \frac{9x}{14} = 9 \]

Step 4: Solve for \(x\)

To solve for \(x\), multiply both sides by 14 to eliminate the fraction: \[ 9x = 126 \] Then, divide both sides by 9: \[ x = \frac{126}{9} = 14 \]

Final Answer

\[ \boxed{x = 14} \]

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