`(2(m+4)+13)/(5)=(21-(8-3m))/(4)`
In the equation above, what is the value of m?

Answer

To solve the equation \((2(m+4)+13)/(5)=(21-(8-3m))/(4)\), we will follow these steps:

### Step 1: Simplify both sides of the equation
First, we simplify the left side:
\[ 2(m+4) + 13 = 2m + 8 + 13 = 2m + 21 \]
So the left side becomes:
\[ \frac{2m + 21}{5} \]

Now simplify the right side:
\[ 21 - (8 - 3m) = 21 - 8 + 3m = 13 + 3m \]
So the right side becomes:
\[ \frac{13 + 3m}{4} \]

Now our equation looks like this:
\[ \frac{2m + 21}{5} = \frac{13 + 3m}{4} \]

### Step 2: Cross-multiply
To eliminate the fractions, we cross-multiply:
\[ 4(2m + 21) = 5(13 + 3m) \]

### Step 3: Distribute on both sides
Now we distribute:
\[ 8m + 84 = 65 + 15m \]

### Step 4: Rearrange the equation
Next, we will rearrange the equation to isolate the variable \(m\). Subtract \(8m\) from both sides:
\[ 84 = 65 + 15m - 8m \]
This simplifies to:
\[ 84 = 65 + 7m \]

### Step 5: Isolate \(m\)
Now, subtract \(65\) from both sides:
\[ 84 - 65 = 7m \]
This gives us:
\[ 19 = 7m \]

### Step 6: Solve for \(m\)
Finally, divide both sides by \(7\):
\[ m = \frac{19}{7} \]

Thus, the value of \(m\) is:
\[ \boxed{\frac{19}{7}} \]