Solve the following equations :
`(2x-13)/(5)-(x-3)/(11)=(x-9)/(5)+1`

Answer

To solve the equation \((2x - 13)/5 - (x - 3)/11 = (x - 9)/5 + 1\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can find the least common multiple (LCM) of the denominators (5 and 11). The LCM of 5 and 11 is 55. We will multiply every term in the equation by 55.

\[ 55 \left(\frac{2x - 13}{5}\right) - 55 \left(\frac{x - 3}{11}\right) = 55 \left(\frac{x - 9}{5}\right) + 55(1) \]

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

\[ 11(2x - 13) - 5(x - 3) = 11(x - 9) + 55 \]

Expanding each term:

\[ 22x - 143 - 5x + 15 = 11x - 99 + 55 \]

### Step 3: Combine like terms
Now, combine like terms on both sides:

Left side:
\[ (22x - 5x) + (-143 + 15) = 17x - 128 \]

Right side:
\[ 11x - 99 + 55 = 11x - 44 \]

So, we have:
\[ 17x - 128 = 11x - 44 \]

### Step 4: Isolate the variable
Next, we will isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side:

\[ 17x - 11x = -44 + 128 \]

This simplifies to:
\[ 6x = 84 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 6 to solve for \(x\):

\[ x = \frac{84}{6} = 14 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{14} \]

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