Solve the following equations.Check your result in each case
`x/2+x/4=1/8`

Answer

To solve the equation \( \frac{x}{2} + \frac{x}{4} = \frac{1}{8} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
The denominators in the equation are 2 and 4. The LCM of 2 and 4 is 4.

### Step 2: Rewrite the Equation
We can rewrite the equation by expressing each term with the common denominator of 4:
\[ \frac{x}{2} = \frac{2x}{4} \]
So, the equation becomes:
\[ \frac{2x}{4} + \frac{x}{4} = \frac{1}{8} \]

### Step 3: Combine the Left Side
Now, combine the fractions on the left side:
\[ \frac{2x + x}{4} = \frac{1}{8} \]
This simplifies to:
\[ \frac{3x}{4} = \frac{1}{8} \]

### Step 4: Cross Multiply
To eliminate the fractions, we can cross-multiply:
\[ 3x \cdot 8 = 1 \cdot 4 \]
This gives us:
\[ 24x = 4 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 24 to isolate \( x \):
\[ x = \frac{4}{24} = \frac{1}{6} \]

### Step 6: Check the Result
To check if our solution is correct, substitute \( x = \frac{1}{6} \) back into the original equation:
\[ \frac{1/6}{2} + \frac{1/6}{4} = \frac{1}{8} \]
Calculating each term:
\[ \frac{1}{6} \div 2 = \frac{1}{12} \quad \text{and} \quad \frac{1}{6} \div 4 = \frac{1}{24} \]
Now, add these two fractions:
\[ \frac{1}{12} + \frac{1}{24} \]
To add these, find the LCM of 12 and 24, which is 24:
\[ \frac{1}{12} = \frac{2}{24} \]
So,
\[ \frac{2}{24} + \frac{1}{24} = \frac{3}{24} = \frac{1}{8} \]
Since both sides of the equation are equal, our solution is verified.

### Final Solution
Thus, the solution to the equation \( \frac{x}{2} + \frac{x}{4} = \frac{1}{8} \) is:
\[ x = \frac{1}{6} \]