To solve the equation 5x - 14/7 - 1/2 = 3x - 1/14, we need to simplify both sides of the equation and then isolate the variable x.

**Step 1: Simplify the equation**
We can simplify the equation by combining like terms. Let's start by simplifying the left side of the equation.

5x - 14/7 - 1/2 = 3x - 1/14

First, let's simplify the fractions on the left side of the equation. The fractions have different denominators, so we need to find a common denominator.

The common denominator for 7 and 2 is 14. Therefore, we rewrite the equation as:

5x - (14/7 * 2/2) - 1/2 = 3x - 1/14

Simplifying further:

5x - 28/14 - 1/2 = 3x - 1/14

Next, let's simplify the fractions:

5x - 2 - 7/14 = 3x - 1/14

Simplifying further:

5x - 2 - 1/2 = 3x - 1/14

To simplify the equation even further, let's rewrite the whole numbers as fractions:

5x - 2/1 - 1/2 = 3x - 1/14

Now, let's find a common denominator for the fractions on the left side:

The common denominator for 1 and 2 is 2. Therefore, we rewrite the equation as:

5x - (2/1 * 2/2) - 1/2 = 3x - 1/14

Simplifying further:

5x - 4/2 - 1/2 = 3x - 1/14

Next, let's simplify the fractions:

5x - 2 - 1/2 = 3x - 1/14

Simplifying further:

5x - 2 - 0.5 = 3x - 1/14

Now, we can simplify the equation to:

5x - 2.5 = 3x - 1/14

**Step 2: Isolate the variable x**
To isolate the variable x, we need to get rid of the constants on the right side of the equation. We can do this by subtracting 3x from both sides of the equation:

5x - 2.5 - 3x = -1/14

Simplifying:

2x - 2.5 = -1/14

Next, let's get rid of the decimal on the right side of the equation by multiplying both sides by 14:

14 * (2x - 2.5) = 14 * (-1/14)

Simplifying:

28x - 35 = -1

Now, let's isolate the variable x by adding 35 to both sides of the equation:

28x - 35 + 35 = -1 + 35

Simplifying:

28x = 34

Finally, divide both sides of the equation by 28 to solve for x:

(28x)/28 = 34/28

Simplifying:

x = 17/14

Therefore, the solution to the equation 5x