Final answer:
To solve the equation (1)/(4x) + (1)/(2x) = (x)/(2), we find the common denominator, combine the fractions, and then cross-multiply to solve for x. The solution is x = (3)/(2).
Step-by-step explanation:
To solve the equation (1)/(4x) + (1)/(2x) = (x)/(2), we need to find the value of x that satisfies the equation. First, we'll find the common denominator, which is 4x. Multiplying the numerator and denominator of the first fraction by 2 gives us (2)/(8x). Multiplying the numerator and denominator of the second fraction by 4 gives us (4)/(8x). Combining the fractions, we have (2)/(8x) + (4)/(8x) = (x)/(2). Simplifying this expression gives us (6)/(8x) = (x)/(2).
Next, we'll cross-multiply by multiplying both sides of the equation by 8x, giving us (6) = (4)(x). Simplifying further gives us 6 = 4x. Dividing both sides by 4 gives us x = (3)/(2). Therefore, the solution to the equation (1)/(4x) + (1)/(2x) = (x)/(2) is x = (3)/(2).