Final answer:
To solve the given rational equation, multiply both sides of the equation by the least common denominator (LCD) to eliminate the fractions. Then, combine like terms and solve for x.
Step-by-step explanation:
To solve the given rational equation 3x + 1/2 = x - 3/2, we need to isolate the variable x on one side of the equation.
First, let's get rid of the fractions. By multiplying every term in the equation by the least common denominator (LCD) of 2, we can eliminate the fractions. The LCD in this case is 2.
After multiplying, the equation becomes 6x + 1 = 2x - 3.
Next, we can combine like terms by subtracting 2x from both sides of the equation:
4x + 1 = -3.
Now, subtract 1 from both sides:
4x = -4.
Finally, divide both sides by 4:
x = -1.
Learn more about Solving rational equations