Solve for X: 16(1/4x-2) = 3x+1/2 Linear Equation

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

• Step 1: Distribute 16 across the expression inside the parentheses.
• Step 2: Simplify the equation by moving all terms involving $x$ to one side and constant terms to the other side.
• Step 3: Solve for $x$ by isolation through arithmetic manipulation.

Now, let's work through each step:
Step 1: Start by distributing 16 on the left-hand side:

$16 \times \left( \frac{1}{4}x - 2 \right) = 16 \times \frac{1}{4}x - 16 \times 2$

Simplifying each term gives you:

$4x - 32$

Now the equation is:

$4x - 32 = 3x + \frac{1}{2}$

Step 2: Rearrange to collect like terms, move $3x$ to the left side by subtracting it from both sides:

$4x - 3x - 32 = \frac{1}{2}$

This simplifies to:

$x - 32 = \frac{1}{2}$

Step 3: Isolate $x$ by adding 32 to both sides:

$x = \frac{1}{2} + 32$

Converting to a common denominator and performing the addition:

$x = \frac{1}{2} + \frac{64}{2}$ $x = \frac{65}{2}$

Finally, convert this fraction to a mixed number:

$x = 32\frac{1}{2}$

Therefore, the solution to the problem is $x = 32\frac{1}{2}$.