**Solving the Equation: 6.75 + 3/8x = 13 1/4**

In this article, we will solve the equation 6.75 + 3/8x = 13 1/4. This equation involves fractions and decimals, so we need to be careful when solving it.

**Step 1: Convert the Mixed Number to an Improper Fraction**

First, we need to convert the mixed number 13 1/4 to an improper fraction. To do this, we multiply the whole number part (13) by the denominator (4) and then add the numerator (1).

13 1/4 = (13 × 4) + 1 / 4 = 52 + 1 / 4 = 53/4

So, the equation becomes:

6.75 + 3/8x = 53/4

**Step 2: Convert the Decimal to a Fraction**

Next, we need to convert the decimal 6.75 to a fraction. To do this, we divide 6.75 by 1 and then simplify the fraction.

6.75 = 6.75/1 = 675/100 = 27/4

So, the equation becomes:

27/4 + 3/8x = 53/4

**Step 3: Simplify the Equation**

Now, we can simplify the equation by finding a common denominator, which is 8. We can multiply both sides of the equation by 8 to eliminate the fractions.

8(27/4) + 8(3/8)x = 8(53/4) = 54 + 3x = 106

**Step 4: Solve for x**

Finally, we can solve for x by subtracting 54 from both sides of the equation and then dividing both sides by 3.

54 + 3x = 106 3x = 106 - 54 3x = 52 x = 52/3 x = 17 1/3

Therefore, the value of x is 17 1/3.

**Conclusion**

In this article, we solved the equation 6.75 + 3/8x = 13 1/4 by converting the mixed number to an improper fraction, converting the decimal to a fraction, simplifying the equation, and solving for x. The final answer is x = 17 1/3.