Combining Like Terms: Solving 0.5x + 7¼x Step-by-Step

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

• Step 1: Identify the expressions to be combined: $+0.5x$ and $+7\frac{1}{4}x$.
• Step 2: Convert the mixed number $7\frac{1}{4}$ to a decimal or improper fraction.
• Step 3: Perform the addition of coefficients.

Now, let's work through each step:
Step 1: We are given the expressions $+0.5x$ and $+7\frac{1}{4}x$. These need to be combined.

Step 2: Convert the mixed number $7\frac{1}{4}$ to a decimal or improper fraction.
As an improper fraction, $7\frac{1}{4} = \frac{29}{4}$.
As a decimal, $7\frac{1}{4}$ can be approximated to $7.25$.

Step 3: Add the coefficients:
Using decimals: $0.5 + 7.25 = 7.75$.
Using fractions: Convert $0.5$ to $\frac{1}{2}$ and add $\frac{1}{2} + \frac{29}{4}$.

First, convert $\frac{1}{2}$ to have a common denominator with $\frac{29}{4}$, which is $\frac{2}{4}$.
Sum these, $\frac{2}{4} + \frac{29}{4} = \frac{31}{4}$ which simplifies to $7\frac{3}{4}$.

Thus, $(+0.5x)+(+7\frac{1}{4}x) = 7\frac{3}{4}x$.

Therefore, the solution to the problem is $7\frac{3}{4}x$.