Question

12 multiple choice 1 point
what is the solution of $\frac{3}{x} + \frac{1}{2} = \frac{7}{2x}$?
$x = \frac{1}{2}$
no real solutions
$x = 1$
$x = -1$
previous

Explanation:

Step1: Eliminate denominators

Multiply all terms by $2x$ (the least common denominator, $x
eq0$):
$2x \cdot \frac{3}{x} + 2x \cdot \frac{1}{2} = 2x \cdot \frac{7}{2x}$

Step2: Simplify each term

$6 + x = 7$

Step3: Solve for x

Subtract 6 from both sides:
$x = 7 - 6 = 1$

Step4: Verify the solution

Substitute $x=1$ back into the original equation:
$\frac{3}{1} + \frac{1}{2} = \frac{7}{2(1)}$
$\frac{6}{2} + \frac{1}{2} = \frac{7}{2}$, which is true.

Answer:

$x=1$