Solve the equation. $$ \frac{1}{4}+\frac{4}{x}=\frac{5}{12} $$ Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is $$ \} $$. (Simplify your answer.) B. There is no solution.

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UpStudy AI · Accepted Answer

Let's solve the equation:

$$
\frac{1}{4} + \frac{4}{x} = \frac{5}{12}
$$

**Step 1:** Subtract $$\frac{1}{4}$$ from both sides to isolate $$\frac{4}{x}$$:

$$
\frac{4}{x} = \frac{5}{12} - \frac{1}{4}
$$

**Step 2:** Find a common denominator to subtract the fractions on the right side. The common denominator for 12 and 4 is 12:

$$
\frac{5}{12} - \frac{3}{12} = \frac{2}{12} = \frac{1}{6}
$$

So,

$$
\frac{4}{x} = \frac{1}{6}
$$

**Step 3:** Solve for $$x$$ by cross-multiplying:

$$
4 \times 6 = 1 \times x \implies x = 24
$$

**Conclusion:** The solution to the equation is $$x = 24$$.

**Answer:**  
**A.** The solution set is $$ \{24\} $$. 
The solution set is $$ \{24\} $$.

Solve the equation.

Select the correct choice below and fill in any answer boxes in your choice.
A. The solution set is . (Simplify your answer.)
B. There is no solution.

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Solve the equation. Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is . (Simplify your answer.) B. There is no solution.