Solve: `(2m)/(3)+8=(m)/(2)-1`. Check the result.

Answer

To solve the equation \(\frac{2m}{3} + 8 = \frac{m}{2} - 1\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we will find a common denominator. The denominators are 3 and 2, and the least common multiple (LCM) is 6. We will multiply the entire equation by 6.

\[ 6 \left(\frac{2m}{3}\right) + 6(8) = 6\left(\frac{m}{2}\right) - 6(1) \]

### Step 2: Simplify the equation
Now, we simplify each term:

\[ \frac{6 \cdot 2m}{3} + 48 = \frac{6 \cdot m}{2} - 6 \]

This simplifies to:

\[ 4m + 48 = 3m - 6 \]

### Step 3: Move all terms involving \(m\) to one side
Next, we will move \(3m\) to the left side and \(48\) to the right side:

\[ 4m - 3m = -6 - 48 \]

### Step 4: Combine like terms
Now, we combine the like terms:

\[ m = -54 \]

### Step 5: Check the result
To check the result, we will substitute \(m = -54\) back into the original equation:

Left side:

\[ \frac{2(-54)}{3} + 8 = \frac{-108}{3} + 8 = -36 + 8 = -28 \]

Right side:

\[ \frac{-54}{2} - 1 = -27 - 1 = -28 \]

Since both sides are equal, the solution is verified.

### Final Answer:
\[ m = -54 \]

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