Simplifying and Solving: 5x = 1/2 + 3x

To solve this problem, we'll follow these steps:

• Step 1: Subtract $3x$ from both sides of the equation.
• Step 2: Simplify and solve for $x$.

Now, let's work through each step:

Step 1: Subtract $3x$ from both sides
Starting with the equation $5x = \frac{1}{2} + 3x$, subtract $3x$ from both sides to get:
$(5x - 3x) = \frac{1}{2}$.

Step 2: Simplify and solve for $x$
Simplifying the left side yields $2x = \frac{1}{2}$.
Next, divide both sides of the equation by 2 to isolate $x$:
$x = \frac{1}{2} \div 2$.

When dividing $\frac{1}{2}$ by 2, we are effectively finding half of $\frac{1}{2}$, which is:
$x = \frac{1}{4}$.

Therefore, the solution to the problem is $x = \frac{1}{4}$.