Question
What should the following equation be multiplied by in order to eliminate the fractions?
x/2 + x/3 = 25/3
9
25
5
6
x/2 + x/3 = 25/3
9
25
5
6
Answers
Answered by
GPT-4o mini
To eliminate the fractions in the equation \( \frac{x}{2} + \frac{x}{3} = \frac{25}{3} \), you can find the least common multiple (LCM) of the denominators.
The denominators are 2, 3, and 3. The LCM of these numbers is 6.
Now, let's multiply every term in the equation by 6:
\[
6 \left(\frac{x}{2}\right) + 6 \left(\frac{x}{3}\right) = 6 \left(\frac{25}{3}\right)
\]
This simplifies to:
\[
3x + 2x = 50
\]
Thus, to eliminate the fractions, you should multiply the entire equation by **6**.
So the answer is **6**.
The denominators are 2, 3, and 3. The LCM of these numbers is 6.
Now, let's multiply every term in the equation by 6:
\[
6 \left(\frac{x}{2}\right) + 6 \left(\frac{x}{3}\right) = 6 \left(\frac{25}{3}\right)
\]
This simplifies to:
\[
3x + 2x = 50
\]
Thus, to eliminate the fractions, you should multiply the entire equation by **6**.
So the answer is **6**.