Solve: `0.75x+x/2=0.5x+8`.

Answer

To solve the equation \( 0.75x + \frac{x}{2} = 0.5x + 8 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ 0.75x + \frac{x}{2} = 0.5x + 8 \]

### Step 2: Find a common denominator for the left side
The term \( \frac{x}{2} \) can be rewritten with a common denominator. The least common multiple (LCM) of 1 and 2 is 2. Thus, we can express \( 0.75x \) as \( \frac{0.75 \times 2}{2}x = \frac{1.5x}{2} \).

Now the equation looks like:
\[ \frac{1.5x + x}{2} = 0.5x + 8 \]

### Step 3: Combine the terms in the numerator
Combine the terms in the numerator on the left side:
\[ \frac{1.5x + x}{2} = \frac{2.5x}{2} \]
So now we have:
\[ \frac{2.5x}{2} = 0.5x + 8 \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 2:
\[ 2.5x = 2(0.5x + 8) \]

### Step 5: Distribute on the right side
Distributing on the right side gives:
\[ 2.5x = 1x + 16 \]

### Step 6: Move all terms involving \( x \) to one side
Subtract \( 1x \) from both sides:
\[ 2.5x - 1x = 16 \]
This simplifies to:
\[ 1.5x = 16 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 1.5 to isolate \( x \):
\[ x = \frac{16}{1.5} \]

### Step 8: Simplify the fraction
To simplify \( \frac{16}{1.5} \), we can multiply the numerator and the denominator by 10 to eliminate the decimal:
\[ x = \frac{16 \times 10}{1.5 \times 10} = \frac{160}{15} \]
Now, divide:
\[ x = \frac{160 \div 5}{15 \div 5} = \frac{32}{3} \approx 10.67 \]

### Final Answer
Thus, the solution to the equation is:
\[ x \approx 10.67 \]

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