Solve the following equations and verify the results.
`m/5+m/2-4=(m)/3+7`

Answer

To solve the equation \( \frac{m}{5} + \frac{m}{2} - 4 = \frac{m}{3} + 7 \) and verify the result, we can follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ \frac{m}{5} + \frac{m}{2} - 4 = \frac{m}{3} + 7 \]

### Step 2: Move all terms involving \( m \) to the left side and constant terms to the right side
Rearranging the equation gives us:
\[ \frac{m}{5} + \frac{m}{2} - \frac{m}{3} = 7 + 4 \]
This simplifies to:
\[ \frac{m}{5} + \frac{m}{2} - \frac{m}{3} = 11 \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 5, 2, and 3. The LCM of these numbers is 30.

### Step 4: Rewrite each term with the common denominator
Now we rewrite each fraction with the denominator of 30:
\[ \frac{m}{5} = \frac{6m}{30}, \quad \frac{m}{2} = \frac{15m}{30}, \quad \frac{m}{3} = \frac{10m}{30} \]
Substituting these into the equation gives:
\[ \frac{6m}{30} + \frac{15m}{30} - \frac{10m}{30} = 11 \]

### Step 5: Combine the fractions on the left side
Combining the fractions results in:
\[ \frac{6m + 15m - 10m}{30} = 11 \]
This simplifies to:
\[ \frac{11m}{30} = 11 \]

### Step 6: Eliminate the fraction by multiplying both sides by 30
To eliminate the fraction, multiply both sides by 30:
\[ 11m = 330 \]

### Step 7: Solve for \( m \)
Now, divide both sides by 11:
\[ m = 30 \]

### Step 8: Verify the result
To verify, substitute \( m = 30 \) back into the original equation:
\[ \frac{30}{5} + \frac{30}{2} - 4 = \frac{30}{3} + 7 \]
Calculating each side:
- Left side:
\[ 6 + 15 - 4 = 17 \]
- Right side:
\[ 10 + 7 = 17 \]
Since both sides are equal, the solution is verified.

### Final Answer
The value of \( m \) is \( 30 \).